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Simplifying (4w + -2)(5 + -1w) = 0 Reorder the terms: (-2 + 4w)(5 + -1w) = 0 Multiply (-2 + 4w) * (5 + -1w) (-2(5 + -1w) + 4w * (5 + -1w)) = 0 ((5 * -2 + -1w * -2) + 4w * (5 + -1w)) = 0 ((-10 + 2w) + 4w * (5 + -1w)) = 0 (-10 + 2w + (5 * 4w + -1w * 4w)) = 0 (-10 + 2w + (20w + -4w2)) = 0 Combine like terms: 2w + 20w = 22w (-10 + 22w + -4w2) = 0 Solving -10 + 22w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 11w + -2w2) = 0 Factor a trinomial. 2((-5 + w)(1 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 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 = {5, 0.5}
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