Calculator0
Math Solver
Use our free Math Solver to solve supported equations, algebra and calculus-style problems with step-by-step working that helps you check the result.
Use our free Math Solver to solve supported equations, algebra and calculus-style problems with step-by-step working that helps you check the result.
The fastest way to get a useful result is to tell the solver exactly what mathematical object you are entering. Use an equals sign for equations, explicit operators for multiplication and division, parentheses for grouping, and function notation for supported calculus operations.
| Task | Example input |
|---|---|
| Solve a linear equation | 2x + 5 = 17 |
| Solve a quadratic equation | 4x^2 - 5x - 12 = 0 |
| Expand or simplify | (x + 5)(x + 2) |
| Derivative | d/dx(x^3 + 2x^2) |
| Indefinite integral | integral(x^2 + 3x - 4, x) |
| Limit | limit((x^2 - 1)/(x - 1), x, 1) |
If an input fails, simplify the notation and check parentheses before assuming the mathematics is unsupported.
The current Calculator0 math workspace is aimed at common symbolic and numeric tasks. Its examples cover polynomials, linear and quadratic equations, derivatives, integrals and limits. Support can vary by expression, so the page should be treated as a solver for supported syntax rather than a promise that every advanced problem has a closed-form solution.
A linear equation contains the variable to the first power. The general goal is to isolate the variable by applying the same valid operation to both sides.
To check the solution, substitute x = 6 into the original equation: 2(6) + 5 = 17. Because both sides match, the solution satisfies the equation.
A quadratic equation contains a squared term such as x². Depending on the expression, a solver may factor the polynomial, apply the quadratic formula, or use another symbolic method.
The discriminant b² − 4ac helps describe the type of roots. A positive discriminant gives two distinct real roots, zero gives a repeated real root, and a negative discriminant leads outside the real-number roots.
For polynomial inputs, use explicit exponents and grouping. Writing (x + 5)(x + 2) clearly communicates multiplication between two factors.
A derivative measures how a function changes with respect to a variable. For a simple power, the power rule reduces the exponent by one and multiplies by the original exponent.
A symbolic result can still be wrong if the input was entered incorrectly. Check function parentheses and variable names, especially in products, quotients and nested functions.
An indefinite integral asks for a family of antiderivatives. Because different antiderivatives can differ by a constant, the mathematical result normally includes an arbitrary constant C.
When using the solver, make sure the integration variable is clear. More complicated expressions may require substitution, integration by parts, partial fractions or methods that are not represented by a single elementary form.
A limit describes the value a function approaches as the variable approaches a point. Direct substitution works for many expressions, but indeterminate forms such as 0/0 often require algebraic simplification or another limit technique.
This is a good example of why step-by-step reasoning matters: the original expression is undefined exactly at x = 1, but its limit can still exist.
| Instead of | Prefer | Why |
|---|---|---|
| 2 x | 2*x or 2x if supported | Makes multiplication explicit |
| x2 | x^2 | Makes the exponent clear |
| 1/x+2 | 1/(x+2) when that is intended | Prevents denominator ambiguity |
| sin x | sin(x) | Defines the function argument |
| x+1=5? | x + 1 = 5 | Avoids extra punctuation |
Complex expressions become easier to solve when you build them from smaller, unambiguous pieces. Parentheses are not only formatting—they define the mathematical structure.
A scientific calculator is ideal when the expression is already numeric—for example sin(35°), log(1000) or √72. A math solver is useful when the task is “solve for x,” “factor this polynomial,” “find the derivative,” “integrate,” or “find a limit.”
Math problems naturally group into types such as equations, algebra, calculus, functions and numeric evaluation. Calculator0 keeps the actual tool capabilities explicit so you can choose the right operation without assuming unsupported subjects.
When this happens, retype the problem using standard operators and test a simpler version. This often distinguishes a syntax problem from a genuinely unsupported operation.
The solver recognizes different problem types from the way the expression is written. An equation such as 4x^2 - 5x - 12 = 0 asks for values of the unknown that satisfy the equality. An expression such as (x + 5)(x + 2) is an algebraic expression rather than an equation.
Calculus operations should be entered with the operation made explicit. The examples built into the page include a derivative, an integral and a limit, such as d/dx(x^3 + 2x^2), integral(x^2 + 3x - 4, x) and limit((x^2 - 1)/(x - 1), x, 1). Using explicit syntax helps the solver understand what you want it to do.
If a problem contains several nested operations, add parentheses around the intended numerator, denominator, exponent or function argument before solving.
A step-by-step answer is most valuable when you can test it. For an equation, substitute the proposed solution into the original equation and check that both sides become equal. For a derivative, differentiate a simplified equivalent expression independently when practical. For an integral, differentiate the antiderivative to see whether it returns the original integrand (allowing for the constant of integration).
For limits, compare the symbolic result with nearby numeric values when that is mathematically appropriate. The goal is not to repeat every step twice; it is to catch input mistakes, missing parentheses or a result that does not match the original question.
Problems with more than one variable require enough independent information to determine the unknowns. A single equation such as x + y = 10 has infinitely many pairs of solutions, but a second independent equation can make a two-variable system solvable.
If the current solver interface does not accept the exact system notation you need, solve one equation for one variable and substitute it into the other, or reduce the problem to a supported expression. Do not assume a unique answer when the information is insufficient.
Factoring rewrites a polynomial as a product. For x² + 5x + 6, the factors are (x + 2)(x + 3). If the equation is x² + 5x + 6 = 0, the zero-product rule says at least one factor must be zero, giving x = −2 or x = −3.
Factoring is useful because it can expose roots, simplify rational expressions and make limits easier. Multiply the factors back together to verify that the factorization reproduces the original polynomial.
Equations involving square roots can create extraneous solutions when both sides are squared. For example, squaring removes sign information, so every candidate obtained after squaring should be substituted into the original equation before it is accepted.
Exponent rules also depend on the domain. For positive bases, xᵃxᵇ = xᵃ⁺ᵇ and (xᵃ)ᵇ = xᵃᵇ, but expressions with negative bases and fractional exponents may require extra care in the real-number system.
A rational expression contains a variable in a denominator. Values that make the original denominator zero are excluded from the domain even if a factor later cancels. For example, (x²−1)/(x−1) simplifies to x+1 for x ≠ 1, but the original expression remains undefined at x = 1.
When solving equations with fractions, note excluded values first, clear denominators carefully, solve the resulting equation, and then reject any candidate that violates the original domain.
| Rule | Form | Example |
|---|---|---|
| Constant | d/dx(c) = 0 | d/dx(7) = 0 |
| Power | d/dx(xⁿ) = n xⁿ⁻¹ | d/dx(x⁴) = 4x³ |
| Sum | (f+g)' = f' + g' | (x²+sin x)' = 2x + cos x |
| Product | (fg)' = f'g + fg' | (x²eˣ)' = 2xeˣ + x²eˣ |
| Chain | d/dx f(g(x)) = f'(g(x))g'(x) | d/dx sin(x²) = 2x cos(x²) |
The solver can assist with supported derivative inputs, but recognizing the rule helps you interpret and verify the output.
Integration reverses differentiation in many common cases. The power rule gives ∫xⁿdx = xⁿ⁺¹/(n+1) + C for n ≠ −1. The special case ∫1/x dx = ln|x| + C follows a different pattern.
More complicated integrals may require substitution, integration by parts or partial fractions. The simplest verification is to differentiate the proposed antiderivative. If the derivative returns the original integrand on the relevant domain, the result is consistent.
Direct substitution works when a function is continuous at the point of interest. If substitution produces 0/0, the form is indeterminate rather than the final answer. Algebraic simplification, factoring or rationalization may reveal the limiting value.
A function can have a limit at a point even when the original expression is undefined exactly at that point.
An exact result preserves mathematical structure, such as √2, π/3 or 5/7. A decimal approximation is often easier to use numerically but may lose information through rounding. Keep exact forms when doing symbolic work and convert to decimals when a measurement or numerical estimate is required.
If two answers look different, simplify both before deciding they disagree. For example, 1/√2 and √2/2 represent the same positive real number.
If f(x) = x² − 3x + 2, evaluating f(5) means replacing every x with 5: 25 − 15 + 2 = 12. Parentheses are essential when substituting negative values. If x = −2, write (−2)² rather than −2² when the entire negative number is intended as the base.
Function notation is not multiplication: f(x) names the output of the function f for input x. Keeping that distinction clear helps when differentiating, composing or evaluating functions.
The solver can handle the mathematical expression you enter, but turning a word problem into the correct equation still requires choosing the right relationships.
Enter the equation or expression with clear operators and parentheses, run the solver, then review the result and available working.
Yes. It is designed for supported equations and algebraic expressions, including common linear and quadratic examples.
For supported equation forms, enter the equation with an equals sign and the solver can attempt to isolate the variable.
The math workspace includes supported derivative operations and derivative examples.
It supports symbolic integration for expressions handled by the underlying math engine; some advanced integrals may not have a simple elementary result.
Yes, supported limit syntax is included in the tool examples.
Use explicit parentheses, operators, exponents and function notation so the structure is unambiguous.
The notation may be ambiguous, the expression may be unsupported, or the problem may require assumptions the solver does not have.
Substitute the proposed value back into the original equation and verify that both sides are equal.
Math Solver targets supported symbolic problems and equations; Scientific Calculator is optimized for numeric scientific expressions.
It is a candidate produced by algebraic manipulation that does not satisfy the original equation, so it must be rejected after checking.
A simplified expression can hide values that made the original denominator zero or otherwise made the original problem undefined.
Yes. Exact expressions can often be rewritten in equivalent forms, so simplify or substitute before deciding they disagree.
Differentiate the proposed antiderivative and check that it returns the original integrand on the relevant domain.
It is an indeterminate form, not the final limit; the expression may need factoring, rationalization or another method.