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Simplifying (3x + 6)(9 + 2x) = 0 Reorder the terms: (6 + 3x)(9 + 2x) = 0 Multiply (6 + 3x) * (9 + 2x) (6(9 + 2x) + 3x * (9 + 2x)) = 0 ((9 * 6 + 2x * 6) + 3x * (9 + 2x)) = 0 ((54 + 12x) + 3x * (9 + 2x)) = 0 (54 + 12x + (9 * 3x + 2x * 3x)) = 0 (54 + 12x + (27x + 6x2)) = 0 Combine like terms: 12x + 27x = 39x (54 + 39x + 6x2) = 0 Solving 54 + 39x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(18 + 13x + 2x2) = 0 Factor a trinomial. 3((9 + 2x)(2 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-4.5, -2}
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