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Simplifying w(w + 2) = w(10 + -1w) Reorder the terms: w(2 + w) = w(10 + -1w) (2 * w + w * w) = w(10 + -1w) (2w + w2) = w(10 + -1w) 2w + w2 = (10 * w + -1w * w) 2w + w2 = (10w + -1w2) Solving 2w + w2 = 10w + -1w2 Solving for variable 'w'. Reorder the terms: 2w + -10w + w2 + w2 = 10w + -1w2 + -10w + w2 Combine like terms: 2w + -10w = -8w -8w + w2 + w2 = 10w + -1w2 + -10w + w2 Combine like terms: w2 + w2 = 2w2 -8w + 2w2 = 10w + -1w2 + -10w + w2 Reorder the terms: -8w + 2w2 = 10w + -10w + -1w2 + w2 Combine like terms: 10w + -10w = 0 -8w + 2w2 = 0 + -1w2 + w2 -8w + 2w2 = -1w2 + w2 Combine like terms: -1w2 + w2 = 0 -8w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2w'. 2w(-4 + w) = 0 Ignore the factor 2.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 '(-4 + w)' equal to zero and attempt to solve: Simplifying -4 + w = 0 Solving -4 + w = 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 + w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + w = 0 + 4 w = 0 + 4 Combine like terms: 0 + 4 = 4 w = 4 Simplifying w = 4Solution
w = {0, 4}
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