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Simplifying 5w(w + -6)(w + -1) = 0 Reorder the terms: 5w(-6 + w)(w + -1) = 0 Reorder the terms: 5w(-6 + w)(-1 + w) = 0 Multiply (-6 + w) * (-1 + w) 5w(-6(-1 + w) + w(-1 + w)) = 0 5w((-1 * -6 + w * -6) + w(-1 + w)) = 0 5w((6 + -6w) + w(-1 + w)) = 0 5w(6 + -6w + (-1 * w + w * w)) = 0 5w(6 + -6w + (-1w + w2)) = 0 Combine like terms: -6w + -1w = -7w 5w(6 + -7w + w2) = 0 (6 * 5w + -7w * 5w + w2 * 5w) = 0 (30w + -35w2 + 5w3) = 0 Solving 30w + -35w2 + 5w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w'. 5w(6 + -7w + w2) = 0 Factor a trinomial. 5w((1 + -1w)(6 + -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 '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 3
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Solution
w = {0, 1, 6}
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