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Simplifying 3(4x + 9)(x + 5) = 0 Reorder the terms: 3(9 + 4x)(x + 5) = 0 Reorder the terms: 3(9 + 4x)(5 + x) = 0 Multiply (9 + 4x) * (5 + x) 3(9(5 + x) + 4x * (5 + x)) = 0 3((5 * 9 + x * 9) + 4x * (5 + x)) = 0 3((45 + 9x) + 4x * (5 + x)) = 0 3(45 + 9x + (5 * 4x + x * 4x)) = 0 3(45 + 9x + (20x + 4x2)) = 0 Combine like terms: 9x + 20x = 29x 3(45 + 29x + 4x2) = 0 (45 * 3 + 29x * 3 + 4x2 * 3) = 0 (135 + 87x + 12x2) = 0 Solving 135 + 87x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(45 + 29x + 4x2) = 0 Factor a trinomial. 3((5 + x)(9 + 4x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
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 = -2.25Solution
x = {-5, -2.25}
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