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Simplifying (6x2 + -12x)(2x + -6) = 0 Reorder the terms: (-12x + 6x2)(2x + -6) = 0 Reorder the terms: (-12x + 6x2)(-6 + 2x) = 0 Multiply (-12x + 6x2) * (-6 + 2x) (-12x * (-6 + 2x) + 6x2 * (-6 + 2x)) = 0 ((-6 * -12x + 2x * -12x) + 6x2 * (-6 + 2x)) = 0 ((72x + -24x2) + 6x2 * (-6 + 2x)) = 0 (72x + -24x2 + (-6 * 6x2 + 2x * 6x2)) = 0 (72x + -24x2 + (-36x2 + 12x3)) = 0 Combine like terms: -24x2 + -36x2 = -60x2 (72x + -60x2 + 12x3) = 0 Solving 72x + -60x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12x'. 12x(6 + -5x + x2) = 0 Factor a trinomial. 12x((2 + -1x)(3 + -1x)) = 0 Ignore the factor 12.Subproblem 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, 2, 3}
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