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Simplifying (6x + 9)(8x + 1) = 0 Reorder the terms: (9 + 6x)(8x + 1) = 0 Reorder the terms: (9 + 6x)(1 + 8x) = 0 Multiply (9 + 6x) * (1 + 8x) (9(1 + 8x) + 6x * (1 + 8x)) = 0 ((1 * 9 + 8x * 9) + 6x * (1 + 8x)) = 0 ((9 + 72x) + 6x * (1 + 8x)) = 0 (9 + 72x + (1 * 6x + 8x * 6x)) = 0 (9 + 72x + (6x + 48x2)) = 0 Combine like terms: 72x + 6x = 78x (9 + 78x + 48x2) = 0 Solving 9 + 78x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 26x + 16x2) = 0 Factor a trinomial. 3((3 + 2x)(1 + 8x)) = 0 Ignore the factor 3.Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve: Simplifying 1 + 8x = 0 Solving 1 + 8x = 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 + 8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x = 0 + -1 8x = 0 + -1 Combine like terms: 0 + -1 = -1 8x = -1 Divide each side by '8'. x = -0.125 Simplifying x = -0.125Solution
x = {-1.5, -0.125}
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