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Simplifying 128 = (w + 4)(w)(4) Reorder the terms: 128 = (4 + w)(w)(4) Reorder the terms for easier multiplication: 128 = 4w(4 + w) 128 = (4 * 4w + w * 4w) 128 = (16w + 4w2) Solving 128 = 16w + 4w2 Solving for variable 'w'. Reorder the terms: 128 + -16w + -4w2 = 16w + -16w + 4w2 + -4w2 Combine like terms: 16w + -16w = 0 128 + -16w + -4w2 = 0 + 4w2 + -4w2 128 + -16w + -4w2 = 4w2 + -4w2 Combine like terms: 4w2 + -4w2 = 0 128 + -16w + -4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(32 + -4w + -1w2) = 0 Factor a trinomial. 4((4 + -1w)(8 + w)) = 0 Ignore the factor 4.Subproblem 1
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 2
Set the factor '(8 + w)' equal to zero and attempt to solve: Simplifying 8 + w = 0 Solving 8 + w = 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 + w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + w = 0 + -8 w = 0 + -8 Combine like terms: 0 + -8 = -8 w = -8 Simplifying w = -8Solution
w = {4, -8}
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