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Simplifying x(12 + -2x)(18 + -2x) = 0 Multiply (12 + -2x) * (18 + -2x) x(12(18 + -2x) + -2x * (18 + -2x)) = 0 x((18 * 12 + -2x * 12) + -2x * (18 + -2x)) = 0 x((216 + -24x) + -2x * (18 + -2x)) = 0 x(216 + -24x + (18 * -2x + -2x * -2x)) = 0 x(216 + -24x + (-36x + 4x2)) = 0 Combine like terms: -24x + -36x = -60x x(216 + -60x + 4x2) = 0 (216 * x + -60x * x + 4x2 * x) = 0 (216x + -60x2 + 4x3) = 0 Solving 216x + -60x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(54 + -15x + x2) = 0 Factor a trinomial. 4x((6 + -1x)(9 + -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 '(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 = 6Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {0, 6, 9}
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