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Simplifying (4w + 5)(2 + w) = 0 Reorder the terms: (5 + 4w)(2 + w) = 0 Multiply (5 + 4w) * (2 + w) (5(2 + w) + 4w * (2 + w)) = 0 ((2 * 5 + w * 5) + 4w * (2 + w)) = 0 ((10 + 5w) + 4w * (2 + w)) = 0 (10 + 5w + (2 * 4w + w * 4w)) = 0 (10 + 5w + (8w + 4w2)) = 0 Combine like terms: 5w + 8w = 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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