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Simplifying (4w + -2)(4 + -1w) = 0 Reorder the terms: (-2 + 4w)(4 + -1w) = 0 Multiply (-2 + 4w) * (4 + -1w) (-2(4 + -1w) + 4w * (4 + -1w)) = 0 ((4 * -2 + -1w * -2) + 4w * (4 + -1w)) = 0 ((-8 + 2w) + 4w * (4 + -1w)) = 0 (-8 + 2w + (4 * 4w + -1w * 4w)) = 0 (-8 + 2w + (16w + -4w2)) = 0 Combine like terms: 2w + 16w = 18w (-8 + 18w + -4w2) = 0 Solving -8 + 18w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 9w + -2w2) = 0 Factor a trinomial. 2((-4 + w)(1 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + w)' equal to zero and attempt to solve: Simplifying -4 + w = 0 Solving -4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + w = 0 + 4 w = 0 + 4 Combine like terms: 0 + 4 = 4 w = 4 Simplifying w = 4Subproblem 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 = {4, 0.5}
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