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Simplifying (2w + 4)(w) = 1680 Reorder the terms: (4 + 2w)(w) = 1680 Reorder the terms for easier multiplication: w(4 + 2w) = 1680 (4 * w + 2w * w) = 1680 (4w + 2w2) = 1680 Solving 4w + 2w2 = 1680 Solving for variable 'w'. Reorder the terms: -1680 + 4w + 2w2 = 1680 + -1680 Combine like terms: 1680 + -1680 = 0 -1680 + 4w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-840 + 2w + w2) = 0 Factor a trinomial. 2((-30 + -1w)(28 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -1w)' equal to zero and attempt to solve: Simplifying -30 + -1w = 0 Solving -30 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -1w = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1w = 0 + 30 -1w = 0 + 30 Combine like terms: 0 + 30 = 30 -1w = 30 Divide each side by '-1'. w = -30 Simplifying w = -30Subproblem 2
Set the factor '(28 + -1w)' equal to zero and attempt to solve: Simplifying 28 + -1w = 0 Solving 28 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + -1w = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -1w = 0 + -28 -1w = 0 + -28 Combine like terms: 0 + -28 = -28 -1w = -28 Divide each side by '-1'. w = 28 Simplifying w = 28Solution
w = {-30, 28}
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