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Simplifying (2 + w)(4w + 5) = 0 Reorder the terms: (2 + w)(5 + 4w) = 0 Multiply (2 + w) * (5 + 4w) (2(5 + 4w) + w(5 + 4w)) = 0 ((5 * 2 + 4w * 2) + w(5 + 4w)) = 0 ((10 + 8w) + w(5 + 4w)) = 0 (10 + 8w + (5 * w + 4w * w)) = 0 (10 + 8w + (5w + 4w2)) = 0 Combine like terms: 8w + 5w = 13w (10 + 13w + 4w2) = 0 Solving 10 + 13w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (2 + w)(5 + 4w) = 0Subproblem 1
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 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 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Subproblem 2
Set the factor '(5 + 4w)' equal to zero and attempt to solve: Simplifying 5 + 4w = 0 Solving 5 + 4w = 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 + 4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4w = 0 + -5 4w = 0 + -5 Combine like terms: 0 + -5 = -5 4w = -5 Divide each side by '4'. w = -1.25 Simplifying w = -1.25Solution
w = {-2, -1.25}
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