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Simplifying (2w + -5)(9 + w) = 0 Reorder the terms: (-5 + 2w)(9 + w) = 0 Multiply (-5 + 2w) * (9 + w) (-5(9 + w) + 2w * (9 + w)) = 0 ((9 * -5 + w * -5) + 2w * (9 + w)) = 0 ((-45 + -5w) + 2w * (9 + w)) = 0 (-45 + -5w + (9 * 2w + w * 2w)) = 0 (-45 + -5w + (18w + 2w2)) = 0 Combine like terms: -5w + 18w = 13w (-45 + 13w + 2w2) = 0 Solving -45 + 13w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -1w)(5 + -2w) = 0Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 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 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 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 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Solution
w = {-9, 2.5}
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