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Simplifying (x)(6 + -2x)(12 + -2x) = 0 Multiply (6 + -2x) * (12 + -2x) x(6(12 + -2x) + -2x * (12 + -2x)) = 0 x((12 * 6 + -2x * 6) + -2x * (12 + -2x)) = 0 x((72 + -12x) + -2x * (12 + -2x)) = 0 x(72 + -12x + (12 * -2x + -2x * -2x)) = 0 x(72 + -12x + (-24x + 4x2)) = 0 Combine like terms: -12x + -24x = -36x x(72 + -36x + 4x2) = 0 (72 * x + -36x * x + 4x2 * x) = 0 (72x + -36x2 + 4x3) = 0 Solving 72x + -36x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(18 + -9x + x2) = 0 Factor a trinomial. 4x((3 + -1x)(6 + -1x)) = 0 Ignore the factor 4.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 '(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 = 3Subproblem 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, 3, 6}
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