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Simplifying ((w + -1) + w)((w + -2) + 3w) = 0 Reorder the terms: ((-1 + w) + w)((w + -2) + 3w) = 0 Remove parenthesis around (-1 + w) (-1 + w + w)((w + -2) + 3w) = 0 Combine like terms: w + w = 2w (-1 + 2w)((w + -2) + 3w) = 0 Reorder the terms: (-1 + 2w)((-2 + w) + 3w) = 0 Remove parenthesis around (-2 + w) (-1 + 2w)(-2 + w + 3w) = 0 Combine like terms: w + 3w = 4w (-1 + 2w)(-2 + 4w) = 0 Multiply (-1 + 2w) * (-2 + 4w) (-1(-2 + 4w) + 2w * (-2 + 4w)) = 0 ((-2 * -1 + 4w * -1) + 2w * (-2 + 4w)) = 0 ((2 + -4w) + 2w * (-2 + 4w)) = 0 (2 + -4w + (-2 * 2w + 4w * 2w)) = 0 (2 + -4w + (-4w + 8w2)) = 0 Combine like terms: -4w + -4w = -8w (2 + -8w + 8w2) = 0 Solving 2 + -8w + 8w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -4w + 4w2) = 0 Factor a trinomial. 2((1 + -2w)(1 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 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 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5Subproblem 2
Set the factor '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 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 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5Solution
w = {0.5, 0.5}
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