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Simplifying w(3 + w) = w(7 + -1w) (3 * w + w * w) = w(7 + -1w) (3w + w2) = w(7 + -1w) 3w + w2 = (7 * w + -1w * w) 3w + w2 = (7w + -1w2) Solving 3w + w2 = 7w + -1w2 Solving for variable 'w'. Reorder the terms: 3w + -7w + w2 + w2 = 7w + -1w2 + -7w + w2 Combine like terms: 3w + -7w = -4w -4w + w2 + w2 = 7w + -1w2 + -7w + w2 Combine like terms: w2 + w2 = 2w2 -4w + 2w2 = 7w + -1w2 + -7w + w2 Reorder the terms: -4w + 2w2 = 7w + -7w + -1w2 + w2 Combine like terms: 7w + -7w = 0 -4w + 2w2 = 0 + -1w2 + w2 -4w + 2w2 = -1w2 + w2 Combine like terms: -1w2 + w2 = 0 -4w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2w'. 2w(-2 + 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 '(-2 + w)' equal to zero and attempt to solve: Simplifying -2 + w = 0 Solving -2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + w = 0 + 2 w = 0 + 2 Combine like terms: 0 + 2 = 2 w = 2 Simplifying w = 2Solution
w = {0, 2}
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