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Simplifying x3 + -4x2 = 4x2 + -12x Reorder the terms: -4x2 + x3 = 4x2 + -12x Reorder the terms: -4x2 + x3 = -12x + 4x2 Solving -4x2 + x3 = -12x + 4x2 Solving for variable 'x'. Reorder the terms: 12x + -4x2 + -4x2 + x3 = -12x + 4x2 + 12x + -4x2 Combine like terms: -4x2 + -4x2 = -8x2 12x + -8x2 + x3 = -12x + 4x2 + 12x + -4x2 Reorder the terms: 12x + -8x2 + x3 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 12x + -8x2 + x3 = 0 + 4x2 + -4x2 12x + -8x2 + x3 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 12x + -8x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -8x + 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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