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Simplifying 12(x + -6)(2x + 3) = 0 Reorder the terms: 12(-6 + x)(2x + 3) = 0 Reorder the terms: 12(-6 + x)(3 + 2x) = 0 Multiply (-6 + x) * (3 + 2x) 12(-6(3 + 2x) + x(3 + 2x)) = 0 12((3 * -6 + 2x * -6) + x(3 + 2x)) = 0 12((-18 + -12x) + x(3 + 2x)) = 0 12(-18 + -12x + (3 * x + 2x * x)) = 0 12(-18 + -12x + (3x + 2x2)) = 0 Combine like terms: -12x + 3x = -9x 12(-18 + -9x + 2x2) = 0 (-18 * 12 + -9x * 12 + 2x2 * 12) = 0 (-216 + -108x + 24x2) = 0 Solving -216 + -108x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-18 + -9x + 2x2) = 0 Factor a trinomial. 12((-3 + -2x)(6 + -1x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = 6Solution
x = {-1.5, 6}
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