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Simplifying (4x + 6)(9x + 8) = 0 Reorder the terms: (6 + 4x)(9x + 8) = 0 Reorder the terms: (6 + 4x)(8 + 9x) = 0 Multiply (6 + 4x) * (8 + 9x) (6(8 + 9x) + 4x * (8 + 9x)) = 0 ((8 * 6 + 9x * 6) + 4x * (8 + 9x)) = 0 ((48 + 54x) + 4x * (8 + 9x)) = 0 (48 + 54x + (8 * 4x + 9x * 4x)) = 0 (48 + 54x + (32x + 36x2)) = 0 Combine like terms: 54x + 32x = 86x (48 + 86x + 36x2) = 0 Solving 48 + 86x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 43x + 18x2) = 0 Factor a trinomial. 2((3 + 2x)(8 + 9x)) = 0 Ignore the factor 2.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 '(8 + 9x)' equal to zero and attempt to solve: Simplifying 8 + 9x = 0 Solving 8 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 9x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 9x = 0 + -8 9x = 0 + -8 Combine like terms: 0 + -8 = -8 9x = -8 Divide each side by '9'. x = -0.8888888889 Simplifying x = -0.8888888889Solution
x = {-1.5, -0.8888888889}
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