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Simplifying (2w + 9)(4 + w) = 0 Reorder the terms: (9 + 2w)(4 + w) = 0 Multiply (9 + 2w) * (4 + w) (9(4 + w) + 2w * (4 + w)) = 0 ((4 * 9 + w * 9) + 2w * (4 + w)) = 0 ((36 + 9w) + 2w * (4 + w)) = 0 (36 + 9w + (4 * 2w + w * 2w)) = 0 (36 + 9w + (8w + 2w2)) = 0 Combine like terms: 9w + 8w = 17w (36 + 17w + 2w2) = 0 Solving 36 + 17w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (9 + 2w)(4 + w) = 0Subproblem 1
Set the factor '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 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 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Solution
w = {-4.5, -4}
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