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Simplifying (2 + -1w)(2w + 5) = 0 Reorder the terms: (2 + -1w)(5 + 2w) = 0 Multiply (2 + -1w) * (5 + 2w) (2(5 + 2w) + -1w * (5 + 2w)) = 0 ((5 * 2 + 2w * 2) + -1w * (5 + 2w)) = 0 ((10 + 4w) + -1w * (5 + 2w)) = 0 (10 + 4w + (5 * -1w + 2w * -1w)) = 0 (10 + 4w + (-5w + -2w2)) = 0 Combine like terms: 4w + -5w = -1w (10 + -1w + -2w2) = 0 Solving 10 + -1w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (2 + -1w)(5 + 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 '(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 = {2, -2.5}
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