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Simplifying 3(2x + 3)(6x + 9) = 0 Reorder the terms: 3(3 + 2x)(6x + 9) = 0 Reorder the terms: 3(3 + 2x)(9 + 6x) = 0 Multiply (3 + 2x) * (9 + 6x) 3(3(9 + 6x) + 2x * (9 + 6x)) = 0 3((9 * 3 + 6x * 3) + 2x * (9 + 6x)) = 0 3((27 + 18x) + 2x * (9 + 6x)) = 0 3(27 + 18x + (9 * 2x + 6x * 2x)) = 0 3(27 + 18x + (18x + 12x2)) = 0 Combine like terms: 18x + 18x = 36x 3(27 + 36x + 12x2) = 0 (27 * 3 + 36x * 3 + 12x2 * 3) = 0 (81 + 108x + 36x2) = 0 Solving 81 + 108x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(9 + 12x + 4x2) = 0 Factor a trinomial. 9((3 + 2x)(3 + 2x)) = 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 '(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 = {-1.5, -1.5}
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