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Simplifying 0 = 12x2 + 132x + 216 Reorder the terms: 0 = 216 + 132x + 12x2 Solving 0 = 216 + 132x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -216 = -216 -216 + -132x + -12x2 = 216 + 132x + 12x2 + -216 + -132x + -12x2 Reorder the terms: -216 + -132x + -12x2 = 216 + -216 + 132x + -132x + 12x2 + -12x2 Combine like terms: 216 + -216 = 0 -216 + -132x + -12x2 = 0 + 132x + -132x + 12x2 + -12x2 -216 + -132x + -12x2 = 132x + -132x + 12x2 + -12x2 Combine like terms: 132x + -132x = 0 -216 + -132x + -12x2 = 0 + 12x2 + -12x2 -216 + -132x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -216 + -132x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-12'. -12(18 + 11x + x2) = 0 Factor a trinomial. -12((9 + x)(2 + x)) = 0 Ignore the factor -12.Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-9, -2}
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