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Simplifying (w + 4u + -2)(5w + -5) = 0 Reorder the terms: (-2 + 4u + w)(5w + -5) = 0 Reorder the terms: (-2 + 4u + w)(-5 + 5w) = 0 Multiply (-2 + 4u + w) * (-5 + 5w) (-2(-5 + 5w) + 4u * (-5 + 5w) + w(-5 + 5w)) = 0 ((-5 * -2 + 5w * -2) + 4u * (-5 + 5w) + w(-5 + 5w)) = 0 ((10 + -10w) + 4u * (-5 + 5w) + w(-5 + 5w)) = 0 (10 + -10w + (-5 * 4u + 5w * 4u) + w(-5 + 5w)) = 0 (10 + -10w + (-20u + 20uw) + w(-5 + 5w)) = 0 (10 + -10w + -20u + 20uw + (-5 * w + 5w * w)) = 0 (10 + -10w + -20u + 20uw + (-5w + 5w2)) = 0 Reorder the terms: (10 + -20u + 20uw + -10w + -5w + 5w2) = 0 Combine like terms: -10w + -5w = -15w (10 + -20u + 20uw + -15w + 5w2) = 0 Solving 10 + -20u + 20uw + -15w + 5w2 = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -20u + 20uw + -15w + -10 + 5w2 = 0 + -10 Reorder the terms: 10 + -10 + -20u + 20uw + -15w + 5w2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -20u + 20uw + -15w + 5w2 = 0 + -10 -20u + 20uw + -15w + 5w2 = 0 + -10 Combine like terms: 0 + -10 = -10 -20u + 20uw + -15w + 5w2 = -10 Add '15w' to each side of the equation. -20u + 20uw + -15w + 15w + 5w2 = -10 + 15w Combine like terms: -15w + 15w = 0 -20u + 20uw + 0 + 5w2 = -10 + 15w -20u + 20uw + 5w2 = -10 + 15w Add '-5w2' to each side of the equation. -20u + 20uw + 5w2 + -5w2 = -10 + 15w + -5w2 Combine like terms: 5w2 + -5w2 = 0 -20u + 20uw + 0 = -10 + 15w + -5w2 -20u + 20uw = -10 + 15w + -5w2 Reorder the terms: 10 + -20u + 20uw + -15w + 5w2 = -10 + 15w + -5w2 + 10 + -15w + 5w2 Reorder the terms: 10 + -20u + 20uw + -15w + 5w2 = -10 + 10 + 15w + -15w + -5w2 + 5w2 Combine like terms: -10 + 10 = 0 10 + -20u + 20uw + -15w + 5w2 = 0 + 15w + -15w + -5w2 + 5w2 10 + -20u + 20uw + -15w + 5w2 = 15w + -15w + -5w2 + 5w2 Combine like terms: 15w + -15w = 0 10 + -20u + 20uw + -15w + 5w2 = 0 + -5w2 + 5w2 10 + -20u + 20uw + -15w + 5w2 = -5w2 + 5w2 Combine like terms: -5w2 + 5w2 = 0 10 + -20u + 20uw + -15w + 5w2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -4u + 4uw + -3w + w2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -4u + 4uw + -3w + w2)' equal to zero and attempt to solve: Simplifying 2 + -4u + 4uw + -3w + w2 = 0 Solving 2 + -4u + 4uw + -3w + w2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -4u + 4uw + -3w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + -4u + 4uw + -3w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4u + 4uw + -3w + w2 = 0 + -2 -4u + 4uw + -3w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4u + 4uw + -3w + w2 = -2 Add '3w' to each side of the equation. -4u + 4uw + -3w + 3w + w2 = -2 + 3w Combine like terms: -3w + 3w = 0 -4u + 4uw + 0 + w2 = -2 + 3w -4u + 4uw + w2 = -2 + 3w Add '-1w2' to each side of the equation. -4u + 4uw + w2 + -1w2 = -2 + 3w + -1w2 Combine like terms: w2 + -1w2 = 0 -4u + 4uw + 0 = -2 + 3w + -1w2 -4u + 4uw = -2 + 3w + -1w2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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