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Simplifying (2w + 1)(9 + w) = 0 Reorder the terms: (1 + 2w)(9 + w) = 0 Multiply (1 + 2w) * (9 + w) (1(9 + w) + 2w * (9 + w)) = 0 ((9 * 1 + w * 1) + 2w * (9 + w)) = 0 ((9 + 1w) + 2w * (9 + w)) = 0 (9 + 1w + (9 * 2w + w * 2w)) = 0 (9 + 1w + (18w + 2w2)) = 0 Combine like terms: 1w + 18w = 19w (9 + 19w + 2w2) = 0 Solving 9 + 19w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (9 + w)(1 + 2w) = 0Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve: Simplifying 9 + w = 0 Solving 9 + w = 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 + w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + w = 0 + -9 w = 0 + -9 Combine like terms: 0 + -9 = -9 w = -9 Simplifying w = -9Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5Solution
w = {-9, -0.5}
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