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Simplifying 4w3 + -16w2 = 128w Reorder the terms: -16w2 + 4w3 = 128w Solving -16w2 + 4w3 = 128w Solving for variable 'w'. Reorder the terms: -128w + -16w2 + 4w3 = 128w + -128w Combine like terms: 128w + -128w = 0 -128w + -16w2 + 4w3 = 0 Factor out the Greatest Common Factor (GCF), '4w'. 4w(-32 + -4w + w2) = 0 Factor a trinomial. 4w((-4 + -1w)(8 + -1w)) = 0 Ignore the factor 4.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 '(-4 + -1w)' equal to zero and attempt to solve: Simplifying -4 + -1w = 0 Solving -4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1w = 0 + 4 -1w = 0 + 4 Combine like terms: 0 + 4 = 4 -1w = 4 Divide each side by '-1'. w = -4 Simplifying w = -4Subproblem 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, -4, 8}
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