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Simplifying (2w + 9)(5w + -1) = 0 Reorder the terms: (9 + 2w)(5w + -1) = 0 Reorder the terms: (9 + 2w)(-1 + 5w) = 0 Multiply (9 + 2w) * (-1 + 5w) (9(-1 + 5w) + 2w * (-1 + 5w)) = 0 ((-1 * 9 + 5w * 9) + 2w * (-1 + 5w)) = 0 ((-9 + 45w) + 2w * (-1 + 5w)) = 0 (-9 + 45w + (-1 * 2w + 5w * 2w)) = 0 (-9 + 45w + (-2w + 10w2)) = 0 Combine like terms: 45w + -2w = 43w (-9 + 43w + 10w2) = 0 Solving -9 + 43w + 10w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -2w)(1 + -5w) = 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 '(1 + -5w)' equal to zero and attempt to solve: Simplifying 1 + -5w = 0 Solving 1 + -5w = 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 + -5w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5w = 0 + -1 -5w = 0 + -1 Combine like terms: 0 + -1 = -1 -5w = -1 Divide each side by '-5'. w = 0.2 Simplifying w = 0.2Solution
w = {-4.5, 0.2}
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