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Simplifying 2w(4w + -1) = w(1 + -4w) Reorder the terms: 2w(-1 + 4w) = w(1 + -4w) (-1 * 2w + 4w * 2w) = w(1 + -4w) (-2w + 8w2) = w(1 + -4w) -2w + 8w2 = (1 * w + -4w * w) -2w + 8w2 = (1w + -4w2) Solving -2w + 8w2 = 1w + -4w2 Solving for variable 'w'. Reorder the terms: -2w + -1w + 8w2 + 4w2 = 1w + -4w2 + -1w + 4w2 Combine like terms: -2w + -1w = -3w -3w + 8w2 + 4w2 = 1w + -4w2 + -1w + 4w2 Combine like terms: 8w2 + 4w2 = 12w2 -3w + 12w2 = 1w + -4w2 + -1w + 4w2 Reorder the terms: -3w + 12w2 = 1w + -1w + -4w2 + 4w2 Combine like terms: 1w + -1w = 0 -3w + 12w2 = 0 + -4w2 + 4w2 -3w + 12w2 = -4w2 + 4w2 Combine like terms: -4w2 + 4w2 = 0 -3w + 12w2 = 0 Factor out the Greatest Common Factor (GCF), '3w'. 3w(-1 + 4w) = 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 '(-1 + 4w)' equal to zero and attempt to solve: Simplifying -1 + 4w = 0 Solving -1 + 4w = 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 + 4w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4w = 0 + 1 4w = 0 + 1 Combine like terms: 0 + 1 = 1 4w = 1 Divide each side by '4'. w = 0.25 Simplifying w = 0.25Solution
w = {0, 0.25}
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