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Simplifying 2w2(w + -6) = 54w Reorder the terms: 2w2(-6 + w) = 54w (-6 * 2w2 + w * 2w2) = 54w (-12w2 + 2w3) = 54w Solving -12w2 + 2w3 = 54w Solving for variable 'w'. Reorder the terms: -54w + -12w2 + 2w3 = 54w + -54w Combine like terms: 54w + -54w = 0 -54w + -12w2 + 2w3 = 0 Factor out the Greatest Common Factor (GCF), '2w'. 2w(-27 + -6w + w2) = 0 Factor a trinomial. 2w((-3 + -1w)(9 + -1w)) = 0 Ignore the factor 2.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 '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 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 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 3
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 = {0, -3, 9}
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