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Simplifying (3x + 9)(2x + 3) = 0 Reorder the terms: (9 + 3x)(2x + 3) = 0 Reorder the terms: (9 + 3x)(3 + 2x) = 0 Multiply (9 + 3x) * (3 + 2x) (9(3 + 2x) + 3x * (3 + 2x)) = 0 ((3 * 9 + 2x * 9) + 3x * (3 + 2x)) = 0 ((27 + 18x) + 3x * (3 + 2x)) = 0 (27 + 18x + (3 * 3x + 2x * 3x)) = 0 (27 + 18x + (9x + 6x2)) = 0 Combine like terms: 18x + 9x = 27x (27 + 27x + 6x2) = 0 Solving 27 + 27x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 9x + 2x2) = 0 Factor a trinomial. 3((3 + x)(3 + 2x)) = 0 Ignore the factor 3.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 '(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 = -1.5Solution
x = {-3, -1.5}
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