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Simplifying (3x + 9)(6x + 3) = 0 Reorder the terms: (9 + 3x)(6x + 3) = 0 Reorder the terms: (9 + 3x)(3 + 6x) = 0 Multiply (9 + 3x) * (3 + 6x) (9(3 + 6x) + 3x * (3 + 6x)) = 0 ((3 * 9 + 6x * 9) + 3x * (3 + 6x)) = 0 ((27 + 54x) + 3x * (3 + 6x)) = 0 (27 + 54x + (3 * 3x + 6x * 3x)) = 0 (27 + 54x + (9x + 18x2)) = 0 Combine like terms: 54x + 9x = 63x (27 + 63x + 18x2) = 0 Solving 27 + 63x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(3 + 7x + 2x2) = 0 Factor a trinomial. 9((3 + x)(1 + 2x)) = 0 Ignore the factor 9.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 '(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 = {-3, -0.5}
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