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Simplifying 6x2 + -6x + -12 = 108 Reorder the terms: -12 + -6x + 6x2 = 108 Solving -12 + -6x + 6x2 = 108 Solving for variable 'x'. Reorder the terms: -12 + -108 + -6x + 6x2 = 108 + -108 Combine like terms: -12 + -108 = -120 -120 + -6x + 6x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -120 + -6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-20 + -1x + x2) = 0 Factor a trinomial. 6((-4 + -1x)(5 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-4, 5}
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