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Simplifying 9(x + -3)(x + 5)(2 + 7) = 0 Reorder the terms: 9(-3 + x)(x + 5)(2 + 7) = 0 Reorder the terms: 9(-3 + x)(5 + x)(2 + 7) = 0 Combine like terms: 2 + 7 = 9 9(-3 + x)(5 + x)(9) = 0 Reorder the terms for easier multiplication: 9 * 9(-3 + x)(5 + x) = 0 Multiply 9 * 9 81(-3 + x)(5 + x) = 0 Multiply (-3 + x) * (5 + x) 81(-3(5 + x) + x(5 + x)) = 0 81((5 * -3 + x * -3) + x(5 + x)) = 0 81((-15 + -3x) + x(5 + x)) = 0 81(-15 + -3x + (5 * x + x * x)) = 0 81(-15 + -3x + (5x + x2)) = 0 Combine like terms: -3x + 5x = 2x 81(-15 + 2x + x2) = 0 (-15 * 81 + 2x * 81 + x2 * 81) = 0 (-1215 + 162x + 81x2) = 0 Solving -1215 + 162x + 81x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '81'. 81(-15 + 2x + x2) = 0 Factor a trinomial. 81((-5 + -1x)(3 + -1x)) = 0 Ignore the factor 81.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-5, 3}
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