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Simplifying (2 + w)(5w + -9) = 0 Reorder the terms: (2 + w)(-9 + 5w) = 0 Multiply (2 + w) * (-9 + 5w) (2(-9 + 5w) + w(-9 + 5w)) = 0 ((-9 * 2 + 5w * 2) + w(-9 + 5w)) = 0 ((-18 + 10w) + w(-9 + 5w)) = 0 (-18 + 10w + (-9 * w + 5w * w)) = 0 (-18 + 10w + (-9w + 5w2)) = 0 Combine like terms: 10w + -9w = 1w (-18 + 1w + 5w2) = 0 Solving -18 + 1w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-2 + -1w)(9 + -5w) = 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 + -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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