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Simplifying -2w(w + 9)(w + 2) = 0 Reorder the terms: -2w(9 + w)(w + 2) = 0 Reorder the terms: -2w(9 + w)(2 + w) = 0 Multiply (9 + w) * (2 + w) -2w(9(2 + w) + w(2 + w)) = 0 -2w((2 * 9 + w * 9) + w(2 + w)) = 0 -2w((18 + 9w) + w(2 + w)) = 0 -2w(18 + 9w + (2 * w + w * w)) = 0 -2w(18 + 9w + (2w + w2)) = 0 Combine like terms: 9w + 2w = 11w -2w(18 + 11w + w2) = 0 (18 * -2w + 11w * -2w + w2 * -2w) = 0 (-36w + -22w2 + -2w3) = 0 Solving -36w + -22w2 + -2w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-2w'. -2w(18 + 11w + w2) = 0 Factor a trinomial. -2w((9 + w)(2 + w)) = 0 Ignore the factor -2.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 '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {0, -9, -2}
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