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Simplifying w(w + -5)(w + 9) = 0 Reorder the terms: w(-5 + w)(w + 9) = 0 Reorder the terms: w(-5 + w)(9 + w) = 0 Multiply (-5 + w) * (9 + w) w(-5(9 + w) + w(9 + w)) = 0 w((9 * -5 + w * -5) + w(9 + w)) = 0 w((-45 + -5w) + w(9 + w)) = 0 w(-45 + -5w + (9 * w + w * w)) = 0 w(-45 + -5w + (9w + w2)) = 0 Combine like terms: -5w + 9w = 4w w(-45 + 4w + w2) = 0 (-45 * w + 4w * w + w2 * w) = 0 (-45w + 4w2 + w3) = 0 Solving -45w + 4w2 + w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(-45 + 4w + w2) = 0 Factor a trinomial. w((-9 + -1w)(5 + -1w)) = 0Subproblem 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 + -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 = -9Subproblem 3
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 = 5Solution
w = {0, -9, 5}
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