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Simplifying (4x + 9)(3x + 6) = 0 Reorder the terms: (9 + 4x)(3x + 6) = 0 Reorder the terms: (9 + 4x)(6 + 3x) = 0 Multiply (9 + 4x) * (6 + 3x) (9(6 + 3x) + 4x * (6 + 3x)) = 0 ((6 * 9 + 3x * 9) + 4x * (6 + 3x)) = 0 ((54 + 27x) + 4x * (6 + 3x)) = 0 (54 + 27x + (6 * 4x + 3x * 4x)) = 0 (54 + 27x + (24x + 12x2)) = 0 Combine like terms: 27x + 24x = 51x (54 + 51x + 12x2) = 0 Solving 54 + 51x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(18 + 17x + 4x2) = 0 Factor a trinomial. 3((9 + 4x)(2 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + 4x)' equal to zero and attempt to solve: Simplifying 9 + 4x = 0 Solving 9 + 4x = 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 + 4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x = 0 + -9 4x = 0 + -9 Combine like terms: 0 + -9 = -9 4x = -9 Divide each side by '4'. x = -2.25 Simplifying x = -2.25Subproblem 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 = {-2.25, -2}
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