Algebra Calculator
Use * for multiplication, ^ for exponents, sqrt() for square roots. Type = to enter an equation.
Enter an Expression or Equation
Type an algebraic expression or equation in the input field above. Use the mode buttons to switch between solving, simplifying, factoring, expanding, or solving systems.
How to Use the Algebra Calculator
Select Your Calculation Mode
Choose from five modes: Solve (for equations like 2x + 5 = 13 or x^2 - 4 = 0), Simplify (to reduce expressions to simplest form), Factor (to decompose polynomials like x^2 + 5x + 6 into factors), Expand (to distribute products like (x+3)(x-2)), or Systems (to solve two simultaneous linear equations). The mode determines how the expression is interpreted and processed.
Enter Your Expression
Type your mathematical expression using standard notation. Use * for multiplication (e.g. 2*x), ^ for exponents (e.g. x^2), and sqrt() for square roots. Use = to write an equation. Click the symbol buttons below the input field to insert special characters, or click any of the example chips to load a sample expression for that mode.
Review the Solution
The answer appears instantly at the top of the results panel. For quadratic equations, the root analysis section shows the discriminant value and classifies the roots (two real, one real, or no real roots). A formula reference box shows any formula applied. For inequalities, a number line visualization shows the solution set graphically.
Expand Step-by-Step Solution
Click the Step-by-Step Solution accordion to see every transformation applied to reach the answer, with the algebraic rule identified at each step. Use this to learn the solution process or verify your own manual work. Export the solution to CSV to save the expression, answer, and step-by-step breakdown, or copy the answer directly to your clipboard.
Frequently Asked Questions
How do I enter a quadratic equation?
Enter quadratic equations in Solve mode using the format ax^2 + bx + c = 0. For example: x^2 - 5x + 6 = 0, or 2x^2 + 3x - 2 = 0. Use the ^ symbol for exponents — you can click the ^ button in the symbol toolbar or type it directly. You can also enter a quadratic that has been rearranged, such as x^2 = 4 or x^2 + 2x = 8, and the calculator will rearrange it to standard form before solving. The calculator will display the discriminant, classify the root type (two real roots, one repeated root, or no real roots), and show both values of x when real solutions exist.
What is the quadratic formula and when is it used?
The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. It is used when a quadratic cannot be factored easily or when you need exact solutions. The expression b² - 4ac under the square root is called the discriminant. If the discriminant is positive, there are two distinct real roots. If it equals zero, there is one repeated root (x = -b/2a). If the discriminant is negative, there are no real roots — the solutions are complex (involving the imaginary number i). The quadratic formula works for any quadratic equation regardless of whether it factors nicely.
How do I solve a system of two equations?
Switch to Systems mode, enter the first equation in the main input field (e.g. 2x + y = 10), and the second equation in the Equation 2 field (e.g. x - y = 2). The calculator solves the system using substitution: it isolates one variable from one equation and substitutes into the other. The result shows the values of both x and y that satisfy both equations simultaneously. A system has a unique solution when the two lines represented by the equations intersect at exactly one point, no solution when the lines are parallel, and infinitely many solutions when the two equations represent the same line.
What does factoring a polynomial mean?
Factoring a polynomial means expressing it as a product of simpler polynomial factors. For example, x² + 5x + 6 factors into (x + 2)(x + 3), because multiplying those binomials gives back the original expression. Factoring is the reverse of expanding. It is useful for solving polynomial equations (set each factor equal to zero to find the roots), simplifying rational expressions (canceling common factors from numerator and denominator), and understanding the behavior of polynomial functions. The calculator handles quadratic trinomials, difference of squares (a² - b² = (a+b)(a-b)), and linear expressions. Enter your polynomial in Factor mode and the calculator returns the factored form with step-by-step explanation.
What is the difference between simplifying and expanding?
Simplifying reduces an expression to its most compact equivalent form by combining like terms, reducing fractions, and applying arithmetic. For example, 3x + 2x - 4 simplifies to 5x - 4. Expanding takes an expression in factored or product form and distributes multiplication to convert it into a sum of terms. For example, (x + 3)(x - 2) expands to x² + x - 6 using the FOIL method (First, Outer, Inner, Last). They are inverse operations: factoring is the reverse of expanding, and simplification reduces the complexity of an already-expanded expression. Use Simplify mode for reducing expressions that are already written as sums and differences. Use Expand mode to distribute products of binomials or polynomials.
How are linear inequalities solved differently from equations?
Linear inequalities are solved using the same inverse operations as linear equations, with one critical difference: when you multiply or divide both sides by a negative number, the direction of the inequality reverses. For example, solving -2x > 8 requires dividing by -2, which flips the > to <, giving x < -4. The calculator handles this automatically and shows the step where the flip occurs. The solution to a linear inequality is a range of values rather than a single number. The number line visualization shows the solution set graphically, using an open circle for strict inequalities (< or >) where the boundary value is not included, and a closed circle for non-strict inequalities (≤ or ≥) where the boundary value is included in the solution.