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Simplifying (3x + 3)(6x + 9) = 0 Reorder the terms: (3 + 3x)(6x + 9) = 0 Reorder the terms: (3 + 3x)(9 + 6x) = 0 Multiply (3 + 3x) * (9 + 6x) (3(9 + 6x) + 3x * (9 + 6x)) = 0 ((9 * 3 + 6x * 3) + 3x * (9 + 6x)) = 0 ((27 + 18x) + 3x * (9 + 6x)) = 0 (27 + 18x + (9 * 3x + 6x * 3x)) = 0 (27 + 18x + (27x + 18x2)) = 0 Combine like terms: 18x + 27x = 45x (27 + 45x + 18x2) = 0 Solving 27 + 45x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(3 + 5x + 2x2) = 0 Factor a trinomial. 9((3 + 2x)(1 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-1.5, -1}
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