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Simplifying 5(w + 3)(-1w + 5) = 0 Reorder the terms: 5(3 + w)(-1w + 5) = 0 Reorder the terms: 5(3 + w)(5 + -1w) = 0 Multiply (3 + w) * (5 + -1w) 5(3(5 + -1w) + w(5 + -1w)) = 0 5((5 * 3 + -1w * 3) + w(5 + -1w)) = 0 5((15 + -3w) + w(5 + -1w)) = 0 5(15 + -3w + (5 * w + -1w * w)) = 0 5(15 + -3w + (5w + -1w2)) = 0 Combine like terms: -3w + 5w = 2w 5(15 + 2w + -1w2) = 0 (15 * 5 + 2w * 5 + -1w2 * 5) = 0 (75 + 10w + -5w2) = 0 Solving 75 + 10w + -5w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(15 + 2w + -1w2) = 0 Factor a trinomial. 5((5 + -1w)(3 + w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {5, -3}
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