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Simplifying 2x(x + -6)(x + -9) = 0 Reorder the terms: 2x(-6 + x)(x + -9) = 0 Reorder the terms: 2x(-6 + x)(-9 + x) = 0 Multiply (-6 + x) * (-9 + x) 2x(-6(-9 + x) + x(-9 + x)) = 0 2x((-9 * -6 + x * -6) + x(-9 + x)) = 0 2x((54 + -6x) + x(-9 + x)) = 0 2x(54 + -6x + (-9 * x + x * x)) = 0 2x(54 + -6x + (-9x + x2)) = 0 Combine like terms: -6x + -9x = -15x 2x(54 + -15x + x2) = 0 (54 * 2x + -15x * 2x + x2 * 2x) = 0 (108x + -30x2 + 2x3) = 0 Solving 108x + -30x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(54 + -15x + x2) = 0 Factor a trinomial. 2x((6 + -1x)(9 + -1x)) = 0 Ignore the factor 2.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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