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Simplifying (2w + 6) * w = 80 Reorder the terms: (6 + 2w) * w = 80 Reorder the terms for easier multiplication: w(6 + 2w) = 80 (6 * w + 2w * w) = 80 (6w + 2w2) = 80 Solving 6w + 2w2 = 80 Solving for variable 'w'. Reorder the terms: -80 + 6w + 2w2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 6w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 3w + w2) = 0 Factor a trinomial. 2((-8 + -1w)(5 + -1w)) = 0 Ignore the factor 2.Subproblem 1
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 = -8Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {-8, 5}
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