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Simplifying x(2x + 6)(3x + -9) = 0 Reorder the terms: x(6 + 2x)(3x + -9) = 0 Reorder the terms: x(6 + 2x)(-9 + 3x) = 0 Multiply (6 + 2x) * (-9 + 3x) x(6(-9 + 3x) + 2x * (-9 + 3x)) = 0 x((-9 * 6 + 3x * 6) + 2x * (-9 + 3x)) = 0 x((-54 + 18x) + 2x * (-9 + 3x)) = 0 x(-54 + 18x + (-9 * 2x + 3x * 2x)) = 0 x(-54 + 18x + (-18x + 6x2)) = 0 Combine like terms: 18x + -18x = 0 x(-54 + 0 + 6x2) = 0 x(-54 + 6x2) = 0 (-54 * x + 6x2 * x) = 0 (-54x + 6x3) = 0 Solving -54x + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-9 + x2) = 0 Factor a difference between two squares. 6x((3 + x)(-3 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Solution
x = {0, -3, 3}
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