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Simplifying 4w(w + 2)(w + 9) = 0 Reorder the terms: 4w(2 + w)(w + 9) = 0 Reorder the terms: 4w(2 + w)(9 + w) = 0 Multiply (2 + w) * (9 + w) 4w(2(9 + w) + w(9 + w)) = 0 4w((9 * 2 + w * 2) + w(9 + w)) = 0 4w((18 + 2w) + w(9 + w)) = 0 4w(18 + 2w + (9 * w + w * w)) = 0 4w(18 + 2w + (9w + w2)) = 0 Combine like terms: 2w + 9w = 11w 4w(18 + 11w + w2) = 0 (18 * 4w + 11w * 4w + w2 * 4w) = 0 (72w + 44w2 + 4w3) = 0 Solving 72w + 44w2 + 4w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4w'. 4w(18 + 11w + w2) = 0 Factor a trinomial. 4w((9 + w)(2 + 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 '(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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