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Simplifying 2w(w + -6) = 32 Reorder the terms: 2w(-6 + w) = 32 (-6 * 2w + w * 2w) = 32 (-12w + 2w2) = 32 Solving -12w + 2w2 = 32 Solving for variable 'w'. Reorder the terms: -32 + -12w + 2w2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -12w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -6w + w2) = 0 Factor a trinomial. 2((-2 + -1w)(8 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2Subproblem 2
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 = {-2, 8}
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