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Simplifying 2(x + -6)(x + -9) + 2x(x + -6) + 2x(x + -9) = 1134 Reorder the terms: 2(-6 + x)(x + -9) + 2x(x + -6) + 2x(x + -9) = 1134 Reorder the terms: 2(-6 + x)(-9 + x) + 2x(x + -6) + 2x(x + -9) = 1134 Multiply (-6 + x) * (-9 + x) 2(-6(-9 + x) + x(-9 + x)) + 2x(x + -6) + 2x(x + -9) = 1134 2((-9 * -6 + x * -6) + x(-9 + x)) + 2x(x + -6) + 2x(x + -9) = 1134 2((54 + -6x) + x(-9 + x)) + 2x(x + -6) + 2x(x + -9) = 1134 2(54 + -6x + (-9 * x + x * x)) + 2x(x + -6) + 2x(x + -9) = 1134 2(54 + -6x + (-9x + x2)) + 2x(x + -6) + 2x(x + -9) = 1134 Combine like terms: -6x + -9x = -15x 2(54 + -15x + x2) + 2x(x + -6) + 2x(x + -9) = 1134 (54 * 2 + -15x * 2 + x2 * 2) + 2x(x + -6) + 2x(x + -9) = 1134 (108 + -30x + 2x2) + 2x(x + -6) + 2x(x + -9) = 1134 Reorder the terms: 108 + -30x + 2x2 + 2x(-6 + x) + 2x(x + -9) = 1134 108 + -30x + 2x2 + (-6 * 2x + x * 2x) + 2x(x + -9) = 1134 108 + -30x + 2x2 + (-12x + 2x2) + 2x(x + -9) = 1134 Reorder the terms: 108 + -30x + 2x2 + -12x + 2x2 + 2x(-9 + x) = 1134 108 + -30x + 2x2 + -12x + 2x2 + (-9 * 2x + x * 2x) = 1134 108 + -30x + 2x2 + -12x + 2x2 + (-18x + 2x2) = 1134 Reorder the terms: 108 + -30x + -12x + -18x + 2x2 + 2x2 + 2x2 = 1134 Combine like terms: -30x + -12x = -42x 108 + -42x + -18x + 2x2 + 2x2 + 2x2 = 1134 Combine like terms: -42x + -18x = -60x 108 + -60x + 2x2 + 2x2 + 2x2 = 1134 Combine like terms: 2x2 + 2x2 = 4x2 108 + -60x + 4x2 + 2x2 = 1134 Combine like terms: 4x2 + 2x2 = 6x2 108 + -60x + 6x2 = 1134 Solving 108 + -60x + 6x2 = 1134 Solving for variable 'x'. Reorder the terms: 108 + -1134 + -60x + 6x2 = 1134 + -1134 Combine like terms: 108 + -1134 = -1026 -1026 + -60x + 6x2 = 1134 + -1134 Combine like terms: 1134 + -1134 = 0 -1026 + -60x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-171 + -10x + x2) = 0 Factor a trinomial. 6((-9 + -1x)(19 + -1x)) = 0 Ignore the factor 6.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 '(19 + -1x)' equal to zero and attempt to solve: Simplifying 19 + -1x = 0 Solving 19 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1x = 0 + -19 -1x = 0 + -19 Combine like terms: 0 + -19 = -19 -1x = -19 Divide each side by '-1'. x = 19 Simplifying x = 19Solution
x = {-9, 19}
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