Solves a linear or quadratic equation in one variable (x) and returns every step: expanding parentheses, combining like terms, moving terms across the equals sign, and (for quadratics) applying the quadratic formula.
Use this whenever you need to solve "ax + b = cx + d" or "ax^2 + bx + c = 0" style equations, or check a step-by-step algebra solution someone else produced.
Do not solve this kind of equation by reasoning through it token by token: the two places language models most often go quietly wrong are (1) the sign when distributing a negative across parentheses, e.g. "5 - (x - 3)" losing the minus on the 3, and (2) dropping one of the two ± roots of a quadratic, or rounding a complex root into a false "no solution". This tool always gets both right because it does exact fraction arithmetic, not floating-point guessing, and reports every root it finds — including complex ones, explicitly labeled as complex.
Input: a single string containing exactly one "=", using x (or X) as the only variable, e.g. "3(x-2) = 5x + 4" or "(x+1)(x-3) = 2x^2 - 5". Numbers may be integers or decimals. Implicit multiplication is fine ("3x", "2(x+1)"). Exponents may only be "^2" on the bare variable — "(x+1)^2" is not supported; write "(x+1)(x+1)" instead.
Refuses rather than guesses on: no "=" or more than one, a second variable or a function name (sin, sqrt, log), a "/" anywhere (rewrite as a decimal), an unsupported exponent, an equation that expands past degree 2, unbalanced parentheses, or an inequality (<, >). Every refusal includes a fixHint saying exactly what to change.
Returns the equation type (linear, quadratic, identity, or contradiction), the standard form, the full list of steps, the solution(s) as exact fractions (with a decimal alongside when not a whole number), and a disclaimer that this covers only one-variable linear and quadratic equations.
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