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Simplifying 2x(x + -6)(3x + -9) = 0 Reorder the terms: 2x(-6 + x)(3x + -9) = 0 Reorder the terms: 2x(-6 + x)(-9 + 3x) = 0 Multiply (-6 + x) * (-9 + 3x) 2x(-6(-9 + 3x) + x(-9 + 3x)) = 0 2x((-9 * -6 + 3x * -6) + x(-9 + 3x)) = 0 2x((54 + -18x) + x(-9 + 3x)) = 0 2x(54 + -18x + (-9 * x + 3x * x)) = 0 2x(54 + -18x + (-9x + 3x2)) = 0 Combine like terms: -18x + -9x = -27x 2x(54 + -27x + 3x2) = 0 (54 * 2x + -27x * 2x + 3x2 * 2x) = 0 (108x + -54x2 + 6x3) = 0 Solving 108x + -54x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(18 + -9x + x2) = 0 Factor a trinomial. 6x((3 + -1x)(6 + -1x)) = 0 Ignore the factor 6.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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