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Simplifying (4x + 12)(8x + 9) = 0 Reorder the terms: (12 + 4x)(8x + 9) = 0 Reorder the terms: (12 + 4x)(9 + 8x) = 0 Multiply (12 + 4x) * (9 + 8x) (12(9 + 8x) + 4x * (9 + 8x)) = 0 ((9 * 12 + 8x * 12) + 4x * (9 + 8x)) = 0 ((108 + 96x) + 4x * (9 + 8x)) = 0 (108 + 96x + (9 * 4x + 8x * 4x)) = 0 (108 + 96x + (36x + 32x2)) = 0 Combine like terms: 96x + 36x = 132x (108 + 132x + 32x2) = 0 Solving 108 + 132x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(27 + 33x + 8x2) = 0 Factor a trinomial. 4((3 + x)(9 + 8x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(9 + 8x)' equal to zero and attempt to solve: Simplifying 9 + 8x = 0 Solving 9 + 8x = 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 + 8x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x = 0 + -9 8x = 0 + -9 Combine like terms: 0 + -9 = -9 8x = -9 Divide each side by '8'. x = -1.125 Simplifying x = -1.125Solution
x = {-3, -1.125}
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