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Simplifying -5(w + -9)(-1w + -1) = 0 Reorder the terms: -5(-9 + w)(-1w + -1) = 0 Reorder the terms: -5(-9 + w)(-1 + -1w) = 0 Multiply (-9 + w) * (-1 + -1w) -5(-9(-1 + -1w) + w(-1 + -1w)) = 0 -5((-1 * -9 + -1w * -9) + w(-1 + -1w)) = 0 -5((9 + 9w) + w(-1 + -1w)) = 0 -5(9 + 9w + (-1 * w + -1w * w)) = 0 -5(9 + 9w + (-1w + -1w2)) = 0 Combine like terms: 9w + -1w = 8w -5(9 + 8w + -1w2) = 0 (9 * -5 + 8w * -5 + -1w2 * -5) = 0 (-45 + -40w + 5w2) = 0 Solving -45 + -40w + 5w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -8w + w2) = 0 Factor a trinomial. 5((-1 + -1w)(9 + -1w)) = 0 Ignore the factor 5.Subproblem 1
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 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 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 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9Solution
w = {-1, 9}
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