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Simplifying (x2 + -4x) * x = 12x Reorder the terms: (-4x + x2) * x = 12x Reorder the terms for easier multiplication: x(-4x + x2) = 12x (-4x * x + x2 * x) = 12x (-4x2 + x3) = 12x Solving -4x2 + x3 = 12x Solving for variable 'x'. Reorder the terms: -12x + -4x2 + x3 = 12x + -12x Combine like terms: 12x + -12x = 0 -12x + -4x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + -4x + x2) = 0 Factor a trinomial. x((-2 + -1x)(6 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, -2, 6}
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