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Simplifying w2 + 4w = 6w + -1w2 Reorder the terms: 4w + w2 = 6w + -1w2 Solving 4w + w2 = 6w + -1w2 Solving for variable 'w'. Reorder the terms: 4w + -6w + w2 + w2 = 6w + -1w2 + -6w + w2 Combine like terms: 4w + -6w = -2w -2w + w2 + w2 = 6w + -1w2 + -6w + w2 Combine like terms: w2 + w2 = 2w2 -2w + 2w2 = 6w + -1w2 + -6w + w2 Reorder the terms: -2w + 2w2 = 6w + -6w + -1w2 + w2 Combine like terms: 6w + -6w = 0 -2w + 2w2 = 0 + -1w2 + w2 -2w + 2w2 = -1w2 + w2 Combine like terms: -1w2 + w2 = 0 -2w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2w'. 2w(-1 + 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 '(-1 + w)' equal to zero and attempt to solve: Simplifying -1 + w = 0 Solving -1 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + w = 0 + 1 w = 0 + 1 Combine like terms: 0 + 1 = 1 w = 1 Simplifying w = 1Solution
w = {0, 1}
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