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Simplifying 12x + 36 + 12x + -36 = 3x2 + -27 Reorder the terms: 36 + -36 + 12x + 12x = 3x2 + -27 Combine like terms: 36 + -36 = 0 0 + 12x + 12x = 3x2 + -27 12x + 12x = 3x2 + -27 Combine like terms: 12x + 12x = 24x 24x = 3x2 + -27 Reorder the terms: 24x = -27 + 3x2 Solving 24x = -27 + 3x2 Solving for variable 'x'. Reorder the terms: 27 + 24x + -3x2 = -27 + 3x2 + 27 + -3x2 Reorder the terms: 27 + 24x + -3x2 = -27 + 27 + 3x2 + -3x2 Combine like terms: -27 + 27 = 0 27 + 24x + -3x2 = 0 + 3x2 + -3x2 27 + 24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 27 + 24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 8x + -1x2) = 0 Factor a trinomial. 3((9 + -1x)(1 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {9, -1}
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