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Simplifying 0 = (12 + -2x)(6 + -2x)(x) Reorder the terms for easier multiplication: 0 = x(12 + -2x)(6 + -2x) Multiply (12 + -2x) * (6 + -2x) 0 = x(12(6 + -2x) + -2x * (6 + -2x)) 0 = x((6 * 12 + -2x * 12) + -2x * (6 + -2x)) 0 = x((72 + -24x) + -2x * (6 + -2x)) 0 = x(72 + -24x + (6 * -2x + -2x * -2x)) 0 = x(72 + -24x + (-12x + 4x2)) Combine like terms: -24x + -12x = -36x 0 = x(72 + -36x + 4x2) 0 = (72 * x + -36x * x + 4x2 * x) 0 = (72x + -36x2 + 4x3) Solving 0 = 72x + -36x2 + 4x3 Solving for variable 'x'. Remove the zero: -72x + 36x2 + -4x3 = 72x + -36x2 + 4x3 + -72x + 36x2 + -4x3 Reorder the terms: -72x + 36x2 + -4x3 = 72x + -72x + -36x2 + 36x2 + 4x3 + -4x3 Combine like terms: 72x + -72x = 0 -72x + 36x2 + -4x3 = 0 + -36x2 + 36x2 + 4x3 + -4x3 -72x + 36x2 + -4x3 = -36x2 + 36x2 + 4x3 + -4x3 Combine like terms: -36x2 + 36x2 = 0 -72x + 36x2 + -4x3 = 0 + 4x3 + -4x3 -72x + 36x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -72x + 36x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-18 + 9x + -1x2) = 0 Factor a trinomial. 4x((-6 + x)(3 + -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 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 3
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 = 3Solution
x = {0, 6, 3}
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