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Simplifying (9 + -1w)(2w + 5) = 0 Reorder the terms: (9 + -1w)(5 + 2w) = 0 Multiply (9 + -1w) * (5 + 2w) (9(5 + 2w) + -1w * (5 + 2w)) = 0 ((5 * 9 + 2w * 9) + -1w * (5 + 2w)) = 0 ((45 + 18w) + -1w * (5 + 2w)) = 0 (45 + 18w + (5 * -1w + 2w * -1w)) = 0 (45 + 18w + (-5w + -2w2)) = 0 Combine like terms: 18w + -5w = 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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