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Simplifying 12w(w + -1) + -2(4w + -2) = 12w + 7 + -2(3 + 4w) + -9 Reorder the terms: 12w(-1 + w) + -2(4w + -2) = 12w + 7 + -2(3 + 4w) + -9 (-1 * 12w + w * 12w) + -2(4w + -2) = 12w + 7 + -2(3 + 4w) + -9 (-12w + 12w2) + -2(4w + -2) = 12w + 7 + -2(3 + 4w) + -9 Reorder the terms: -12w + 12w2 + -2(-2 + 4w) = 12w + 7 + -2(3 + 4w) + -9 -12w + 12w2 + (-2 * -2 + 4w * -2) = 12w + 7 + -2(3 + 4w) + -9 -12w + 12w2 + (4 + -8w) = 12w + 7 + -2(3 + 4w) + -9 Reorder the terms: 4 + -12w + -8w + 12w2 = 12w + 7 + -2(3 + 4w) + -9 Combine like terms: -12w + -8w = -20w 4 + -20w + 12w2 = 12w + 7 + -2(3 + 4w) + -9 4 + -20w + 12w2 = 12w + 7 + (3 * -2 + 4w * -2) + -9 4 + -20w + 12w2 = 12w + 7 + (-6 + -8w) + -9 Reorder the terms: 4 + -20w + 12w2 = 7 + -6 + -9 + 12w + -8w Combine like terms: 7 + -6 = 1 4 + -20w + 12w2 = 1 + -9 + 12w + -8w Combine like terms: 1 + -9 = -8 4 + -20w + 12w2 = -8 + 12w + -8w Combine like terms: 12w + -8w = 4w 4 + -20w + 12w2 = -8 + 4w Solving 4 + -20w + 12w2 = -8 + 4w Solving for variable 'w'. Reorder the terms: 4 + 8 + -20w + -4w + 12w2 = -8 + 4w + 8 + -4w Combine like terms: 4 + 8 = 12 12 + -20w + -4w + 12w2 = -8 + 4w + 8 + -4w Combine like terms: -20w + -4w = -24w 12 + -24w + 12w2 = -8 + 4w + 8 + -4w Reorder the terms: 12 + -24w + 12w2 = -8 + 8 + 4w + -4w Combine like terms: -8 + 8 = 0 12 + -24w + 12w2 = 0 + 4w + -4w 12 + -24w + 12w2 = 4w + -4w Combine like terms: 4w + -4w = 0 12 + -24w + 12w2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(1 + -2w + w2) = 0 Factor a trinomial. 12((1 + -1w)(1 + -1w)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {1, 1}
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