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Simplifying 5w(w + -8)(w + 7) = 0 Reorder the terms: 5w(-8 + w)(w + 7) = 0 Reorder the terms: 5w(-8 + w)(7 + w) = 0 Multiply (-8 + w) * (7 + w) 5w(-8(7 + w) + w(7 + w)) = 0 5w((7 * -8 + w * -8) + w(7 + w)) = 0 5w((-56 + -8w) + w(7 + w)) = 0 5w(-56 + -8w + (7 * w + w * w)) = 0 5w(-56 + -8w + (7w + w2)) = 0 Combine like terms: -8w + 7w = -1w 5w(-56 + -1w + w2) = 0 (-56 * 5w + -1w * 5w + w2 * 5w) = 0 (-280w + -5w2 + 5w3) = 0 Solving -280w + -5w2 + 5w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w'. 5w(-56 + -1w + w2) = 0 Factor a trinomial. 5w((-7 + -1w)(8 + -1w)) = 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 '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 3
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Solution
w = {0, -7, 8}
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