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Simplifying (w + -5)(2w + 4) = 0 Reorder the terms: (-5 + w)(2w + 4) = 0 Reorder the terms: (-5 + w)(4 + 2w) = 0 Multiply (-5 + w) * (4 + 2w) (-5(4 + 2w) + w(4 + 2w)) = 0 ((4 * -5 + 2w * -5) + w(4 + 2w)) = 0 ((-20 + -10w) + w(4 + 2w)) = 0 (-20 + -10w + (4 * w + 2w * w)) = 0 (-20 + -10w + (4w + 2w2)) = 0 Combine like terms: -10w + 4w = -6w (-20 + -6w + 2w2) = 0 Solving -20 + -6w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -3w + w2) = 0 Factor a trinomial. 2((-2 + -1w)(5 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {-2, 5}
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