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Simplifying (2w + -9)(2 + w) = 0 Reorder the terms: (-9 + 2w)(2 + w) = 0 Multiply (-9 + 2w) * (2 + w) (-9(2 + w) + 2w * (2 + w)) = 0 ((2 * -9 + w * -9) + 2w * (2 + w)) = 0 ((-18 + -9w) + 2w * (2 + w)) = 0 (-18 + -9w + (2 * 2w + w * 2w)) = 0 (-18 + -9w + (4w + 2w2)) = 0 Combine like terms: -9w + 4w = -5w (-18 + -5w + 2w2) = 0 Solving -18 + -5w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-2 + -1w)(9 + -2w) = 0Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 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 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2Subproblem 2
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 = 4.5Solution
w = {-2, 4.5}
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