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Simplifying 80 = (2w + 12)(w) Reorder the terms: 80 = (12 + 2w)(w) Reorder the terms for easier multiplication: 80 = w(12 + 2w) 80 = (12 * w + 2w * w) 80 = (12w + 2w2) Solving 80 = 12w + 2w2 Solving for variable 'w'. Reorder the terms: 80 + -12w + -2w2 = 12w + -12w + 2w2 + -2w2 Combine like terms: 12w + -12w = 0 80 + -12w + -2w2 = 0 + 2w2 + -2w2 80 + -12w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 80 + -12w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -6w + -1w2) = 0 Factor a trinomial. 2((4 + -1w)(10 + w)) = 0 Ignore the factor 2.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 '(10 + w)' equal to zero and attempt to solve: Simplifying 10 + w = 0 Solving 10 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + w = 0 + -10 w = 0 + -10 Combine like terms: 0 + -10 = -10 w = -10 Simplifying w = -10Solution
w = {4, -10}
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