Tools / Math / Algebra Solver
Free algebra solver with step-by-step solutions
Use this free algebra calculator with steps to solve for x in linear and quadratic equations. Enter fractions, decimals or brackets, follow the working, and check the answer by substitution. This online equation solver needs no signup or downloads.
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Solution
Use the steps below to understand how the answer is found.
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Step-by-step solution
Decimal answers are rounded to 10 significant digits. Substitution checks may have small floating-point rounding differences.
How to use the algebra solver
Type an equation with one equals sign, select Solve equation, then read the simplified equation, solution and substitution check. You can put x on either side of the equation.
Which equations can I solve?
This tool supports one-variable linear equations, quadratic equations, parentheses, decimal coefficients and division by nonzero constants. Examples include 4x − 8 = 12, (x + 1)^2 = 9 and x/4 + 1 = 3. It also identifies equations with no solution or infinitely many solutions.
Can it solve equations with complex roots?
Yes. When the quadratic discriminant is negative, the answer uses i, where i² = −1. For example, x² + 1 = 0 has solutions x = ±i.
What is not supported yet?
Systems of equations, word problems, inequalities, cubic or higher powers, trigonometric functions, square-root expressions and division by expressions containing x are not supported. The tool explains when an input is outside its scope.
Is the algebra solver free?
Yes. The solver runs directly in your browser, without an API subscription or an account. Use it to check your working and learn the steps.
Equation solver examples: solve for x with steps
This algebra equation calculator handles one unknown, x. These examples show how a one-variable equation solver works, from two-step equations to problems with several operations.
Two step equation calculator with steps
Use the calculator above to solve a two-step equation and check each operation. A two-step equation usually needs two inverse operations to isolate x: first undo addition or subtraction, then undo multiplication or division. Apply the same operation to both sides to keep the equation balanced.
For a fractional coefficient, try (1/2)*x – 3 = 5. Add 3 to both sides to get x/2 = 8, then multiply both sides by 2: x = 16. Check the answer in the original equation: 16/2 – 3 = 5.
Two-step and multi-step linear equation examples
A linear equation has x to the first power. For 2x + 5 = 17, subtract 5 from both sides to get 2x = 12, then divide by 2: x = 6. Substitute 6 into the original equation: 2 × 6 + 5 = 17.
For a multi-step equation such as 3(x − 2) + 4 = 16, expand the brackets to get 3x − 6 + 4 = 16. Combine constants, add 2 to both sides, then divide by 3 to obtain x = 6.
How to solve linear equations with fractions
When fractions have constant denominators, multiply every term on both sides by a common denominator, then isolate x. For x/3 + x/6 = 3, multiply both sides by 6 to obtain 2x + x = 18. Combine like terms to get 3x = 18, so x = 6. Substitution checks the result: 6/3 + 6/6 = 2 + 1 = 3.
For a two-step equation with fractions, enter your equation in the calculator above and follow the working below. Use (1/2)*x for a fractional coefficient. Denominators containing x, such as 1/x, are outside this tool’s scope.
Two-step equations with fractions and decimals
Enter x/3 + 2 = 5 in the equation calculator. Subtract 2, giving x/3 = 3, then multiply both sides by 3: x = 9. To write a fractional coefficient, use (1/2)*x. This fraction equation solver accepts division by constants; it does not accept variable denominators such as 1/x.
For decimals, 0.5x + 1.5 = 4 becomes 0.5x = 2.5, so x = 5. Decimal solutions are rounded for display.
Equation solver with parentheses or brackets
Use round parentheses for grouped terms: 3(x − 2) = 12. Expanding gives 3x − 6 = 12, then 3x = 18 and x = 6. If you call them brackets, enter them as ( ) in this calculator.
Equations with variables on both sides
For 2x + 1 = x + 7, subtract x from each side, then subtract 1: x = 6. An equation solution checker confirms that both sides equal 13 when x is 6.
Quadratic equation solver and quadratic formula calculator
A quadratic equation contains x². Write it as ax² + bx + c = 0 and use the quadratic formula: x = (−b ± √(b² − 4ac)) / (2a). This quadratic equation calculator accepts the complete equation, rather than separate coefficient fields.
For x^2 − 5x + 6 = 0, a = 1, b = −5 and c = 6. The discriminant is 25 − 24 = 1, giving x = (5 ± 1)/2. The quadratic roots are x = 2 and x = 3; both make the original equation equal zero.
Complex roots calculator and repeated roots
For x^2 + 1 = 0, the discriminant is negative, so the solutions are x = ±i, where i² = −1. For x^2 + 2x + 1 = 0, the discriminant is zero and the repeated root is x = −1.
When an equation has no solution or infinitely many solutions
For x = x + 1, cancelling x gives 0 = 1, which is impossible: no solution. For 2x = 2x, both sides are identical, so every value of x is a solution.
A free online algebra calculator without signup
Use this solve-for-x calculator to check homework working or practice an equation. The tool processes your input in your browser and shows the solution check alongside the steps. It supports linear and quadratic equations, not word problems, simultaneous equations, inequalities or photo uploads.