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Simplifying (6x + 3)(9x + 9) = 0 Reorder the terms: (3 + 6x)(9x + 9) = 0 Reorder the terms: (3 + 6x)(9 + 9x) = 0 Multiply (3 + 6x) * (9 + 9x) (3(9 + 9x) + 6x * (9 + 9x)) = 0 ((9 * 3 + 9x * 3) + 6x * (9 + 9x)) = 0 ((27 + 27x) + 6x * (9 + 9x)) = 0 (27 + 27x + (9 * 6x + 9x * 6x)) = 0 (27 + 27x + (54x + 54x2)) = 0 Combine like terms: 27x + 54x = 81x (27 + 81x + 54x2) = 0 Solving 27 + 81x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '27'. 27(1 + 3x + 2x2) = 0 Factor a trinomial. 27((1 + x)(1 + 2x)) = 0 Ignore the factor 27.Subproblem 1
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 = -1Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1, -0.5}
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