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Simplifying (2x + 9)(2x + 6) = 108 Reorder the terms: (9 + 2x)(2x + 6) = 108 Reorder the terms: (9 + 2x)(6 + 2x) = 108 Multiply (9 + 2x) * (6 + 2x) (9(6 + 2x) + 2x * (6 + 2x)) = 108 ((6 * 9 + 2x * 9) + 2x * (6 + 2x)) = 108 ((54 + 18x) + 2x * (6 + 2x)) = 108 (54 + 18x + (6 * 2x + 2x * 2x)) = 108 (54 + 18x + (12x + 4x2)) = 108 Combine like terms: 18x + 12x = 30x (54 + 30x + 4x2) = 108 Solving 54 + 30x + 4x2 = 108 Solving for variable 'x'. Reorder the terms: 54 + -108 + 30x + 4x2 = 108 + -108 Combine like terms: 54 + -108 = -54 -54 + 30x + 4x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -54 + 30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 15x + 2x2) = 0 Factor a trinomial. 2((-9 + -1x)(3 + -2x)) = 0 Ignore the factor 2.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 '(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 = 1.5Solution
x = {-9, 1.5}
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