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Simplifying -4w(w + 9)(w + 5) = 0 Reorder the terms: -4w(9 + w)(w + 5) = 0 Reorder the terms: -4w(9 + w)(5 + w) = 0 Multiply (9 + w) * (5 + w) -4w(9(5 + w) + w(5 + w)) = 0 -4w((5 * 9 + w * 9) + w(5 + w)) = 0 -4w((45 + 9w) + w(5 + w)) = 0 -4w(45 + 9w + (5 * w + w * w)) = 0 -4w(45 + 9w + (5w + w2)) = 0 Combine like terms: 9w + 5w = 14w -4w(45 + 14w + w2) = 0 (45 * -4w + 14w * -4w + w2 * -4w) = 0 (-180w + -56w2 + -4w3) = 0 Solving -180w + -56w2 + -4w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-4w'. -4w(45 + 14w + w2) = 0 Factor a trinomial. -4w((9 + w)(5 + w)) = 0 Ignore the factor -4.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(9 + w)' equal to zero and attempt to solve: Simplifying 9 + w = 0 Solving 9 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + w = 0 + -9 w = 0 + -9 Combine like terms: 0 + -9 = -9 w = -9 Simplifying w = -9Subproblem 3
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Solution
w = {0, -9, -5}
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