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Simplifying (4w + 2)(w) = 210 Reorder the terms: (2 + 4w)(w) = 210 Reorder the terms for easier multiplication: w(2 + 4w) = 210 (2 * w + 4w * w) = 210 (2w + 4w2) = 210 Solving 2w + 4w2 = 210 Solving for variable 'w'. Reorder the terms: -210 + 2w + 4w2 = 210 + -210 Combine like terms: 210 + -210 = 0 -210 + 2w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + w + 2w2) = 0 Factor a trinomial. 2((-15 + -2w)(7 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -2w)' equal to zero and attempt to solve: Simplifying -15 + -2w = 0 Solving -15 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2w = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2w = 0 + 15 -2w = 0 + 15 Combine like terms: 0 + 15 = 15 -2w = 15 Divide each side by '-2'. w = -7.5 Simplifying w = -7.5Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-7.5, 7}
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