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Simplifying w(2w + 1) = 5w(w + 2) Reorder the terms: w(1 + 2w) = 5w(w + 2) (1 * w + 2w * w) = 5w(w + 2) (1w + 2w2) = 5w(w + 2) Reorder the terms: 1w + 2w2 = 5w(2 + w) 1w + 2w2 = (2 * 5w + w * 5w) 1w + 2w2 = (10w + 5w2) Solving 1w + 2w2 = 10w + 5w2 Solving for variable 'w'. Reorder the terms: 1w + -10w + 2w2 + -5w2 = 10w + 5w2 + -10w + -5w2 Combine like terms: 1w + -10w = -9w -9w + 2w2 + -5w2 = 10w + 5w2 + -10w + -5w2 Combine like terms: 2w2 + -5w2 = -3w2 -9w + -3w2 = 10w + 5w2 + -10w + -5w2 Reorder the terms: -9w + -3w2 = 10w + -10w + 5w2 + -5w2 Combine like terms: 10w + -10w = 0 -9w + -3w2 = 0 + 5w2 + -5w2 -9w + -3w2 = 5w2 + -5w2 Combine like terms: 5w2 + -5w2 = 0 -9w + -3w2 = 0 Factor out the Greatest Common Factor (GCF), '-3w'. -3w(3 + w) = 0 Ignore the factor -3.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {0, -3}
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