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Simplifying 5w(w + 4)(w + 5) = 0 Reorder the terms: 5w(4 + w)(w + 5) = 0 Reorder the terms: 5w(4 + w)(5 + w) = 0 Multiply (4 + w) * (5 + w) 5w(4(5 + w) + w(5 + w)) = 0 5w((5 * 4 + w * 4) + w(5 + w)) = 0 5w((20 + 4w) + w(5 + w)) = 0 5w(20 + 4w + (5 * w + w * w)) = 0 5w(20 + 4w + (5w + w2)) = 0 Combine like terms: 4w + 5w = 9w 5w(20 + 9w + w2) = 0 (20 * 5w + 9w * 5w + w2 * 5w) = 0 (100w + 45w2 + 5w3) = 0 Solving 100w + 45w2 + 5w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w'. 5w(20 + 9w + w2) = 0 Factor a trinomial. 5w((5 + w)(4 + w)) = 0 Ignore the factor 5.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 '(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 = -5Subproblem 3
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Solution
w = {0, -5, -4}
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