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Simplifying (6x + 12)(11x + 3) + -1(14x + 13)(6x + 12) = 0 Reorder the terms: (12 + 6x)(11x + 3) + -1(14x + 13)(6x + 12) = 0 Reorder the terms: (12 + 6x)(3 + 11x) + -1(14x + 13)(6x + 12) = 0 Multiply (12 + 6x) * (3 + 11x) (12(3 + 11x) + 6x * (3 + 11x)) + -1(14x + 13)(6x + 12) = 0 ((3 * 12 + 11x * 12) + 6x * (3 + 11x)) + -1(14x + 13)(6x + 12) = 0 ((36 + 132x) + 6x * (3 + 11x)) + -1(14x + 13)(6x + 12) = 0 (36 + 132x + (3 * 6x + 11x * 6x)) + -1(14x + 13)(6x + 12) = 0 (36 + 132x + (18x + 66x2)) + -1(14x + 13)(6x + 12) = 0 Combine like terms: 132x + 18x = 150x (36 + 150x + 66x2) + -1(14x + 13)(6x + 12) = 0 Reorder the terms: 36 + 150x + 66x2 + -1(13 + 14x)(6x + 12) = 0 Reorder the terms: 36 + 150x + 66x2 + -1(13 + 14x)(12 + 6x) = 0 Multiply (13 + 14x) * (12 + 6x) 36 + 150x + 66x2 + -1(13(12 + 6x) + 14x * (12 + 6x)) = 0 36 + 150x + 66x2 + -1((12 * 13 + 6x * 13) + 14x * (12 + 6x)) = 0 36 + 150x + 66x2 + -1((156 + 78x) + 14x * (12 + 6x)) = 0 36 + 150x + 66x2 + -1(156 + 78x + (12 * 14x + 6x * 14x)) = 0 36 + 150x + 66x2 + -1(156 + 78x + (168x + 84x2)) = 0 Combine like terms: 78x + 168x = 246x 36 + 150x + 66x2 + -1(156 + 246x + 84x2) = 0 36 + 150x + 66x2 + (156 * -1 + 246x * -1 + 84x2 * -1) = 0 36 + 150x + 66x2 + (-156 + -246x + -84x2) = 0 Reorder the terms: 36 + -156 + 150x + -246x + 66x2 + -84x2 = 0 Combine like terms: 36 + -156 = -120 -120 + 150x + -246x + 66x2 + -84x2 = 0 Combine like terms: 150x + -246x = -96x -120 + -96x + 66x2 + -84x2 = 0 Combine like terms: 66x2 + -84x2 = -18x2 -120 + -96x + -18x2 = 0 Solving -120 + -96x + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-6'. -6(20 + 16x + 3x2) = 0 Factor a trinomial. -6((10 + 3x)(2 + x)) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(10 + 3x)' equal to zero and attempt to solve: Simplifying 10 + 3x = 0 Solving 10 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3x = 0 + -10 3x = 0 + -10 Combine like terms: 0 + -10 = -10 3x = -10 Divide each side by '3'. x = -3.333333333 Simplifying x = -3.333333333Subproblem 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 = {-3.333333333, -2}
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