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Simplifying (6 + 2w) * w = 216 Reorder the terms for easier multiplication: w(6 + 2w) = 216 (6 * w + 2w * w) = 216 (6w + 2w2) = 216 Solving 6w + 2w2 = 216 Solving for variable 'w'. Reorder the terms: -216 + 6w + 2w2 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + 6w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-108 + 3w + w2) = 0 Factor a trinomial. 2((-12 + -1w)(9 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -1w)' equal to zero and attempt to solve: Simplifying -12 + -1w = 0 Solving -12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1w = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1w = 0 + 12 -1w = 0 + 12 Combine like terms: 0 + 12 = 12 -1w = 12 Divide each side by '-1'. w = -12 Simplifying w = -12Subproblem 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 = 9Solution
w = {-12, 9}
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