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Simplifying (9x + 6)(6x + 9) = 0 Reorder the terms: (6 + 9x)(6x + 9) = 0 Reorder the terms: (6 + 9x)(9 + 6x) = 0 Multiply (6 + 9x) * (9 + 6x) (6(9 + 6x) + 9x * (9 + 6x)) = 0 ((9 * 6 + 6x * 6) + 9x * (9 + 6x)) = 0 ((54 + 36x) + 9x * (9 + 6x)) = 0 (54 + 36x + (9 * 9x + 6x * 9x)) = 0 (54 + 36x + (81x + 54x2)) = 0 Combine like terms: 36x + 81x = 117x (54 + 117x + 54x2) = 0 Solving 54 + 117x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(6 + 13x + 6x2) = 0 Factor a trinomial. 9((3 + 2x)(2 + 3x)) = 0 Ignore the factor 9.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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-1.5, -0.6666666667}
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