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Simplifying (6x + 9)(9x + 3) = 0 Reorder the terms: (9 + 6x)(9x + 3) = 0 Reorder the terms: (9 + 6x)(3 + 9x) = 0 Multiply (9 + 6x) * (3 + 9x) (9(3 + 9x) + 6x * (3 + 9x)) = 0 ((3 * 9 + 9x * 9) + 6x * (3 + 9x)) = 0 ((27 + 81x) + 6x * (3 + 9x)) = 0 (27 + 81x + (3 * 6x + 9x * 6x)) = 0 (27 + 81x + (18x + 54x2)) = 0 Combine like terms: 81x + 18x = 99x (27 + 99x + 54x2) = 0 Solving 27 + 99x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(3 + 11x + 6x2) = 0 Factor a trinomial. 9((3 + 2x)(1 + 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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-1.5, -0.3333333333}
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