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Simplifying (5w + 9)(2 + w) = 0 Reorder the terms: (9 + 5w)(2 + w) = 0 Multiply (9 + 5w) * (2 + w) (9(2 + w) + 5w * (2 + w)) = 0 ((2 * 9 + w * 9) + 5w * (2 + w)) = 0 ((18 + 9w) + 5w * (2 + w)) = 0 (18 + 9w + (2 * 5w + w * 5w)) = 0 (18 + 9w + (10w + 5w2)) = 0 Combine like terms: 9w + 10w = 19w (18 + 19w + 5w2) = 0 Solving 18 + 19w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (2 + w)(9 + 5w) = 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 '(9 + 5w)' equal to zero and attempt to solve: Simplifying 9 + 5w = 0 Solving 9 + 5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5w = 0 + -9 5w = 0 + -9 Combine like terms: 0 + -9 = -9 5w = -9 Divide each side by '5'. w = -1.8 Simplifying w = -1.8Solution
w = {-2, -1.8}
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