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Simplifying (2w + -3)(5w + 5) = 6w + -9 Reorder the terms: (-3 + 2w)(5w + 5) = 6w + -9 Reorder the terms: (-3 + 2w)(5 + 5w) = 6w + -9 Multiply (-3 + 2w) * (5 + 5w) (-3(5 + 5w) + 2w * (5 + 5w)) = 6w + -9 ((5 * -3 + 5w * -3) + 2w * (5 + 5w)) = 6w + -9 ((-15 + -15w) + 2w * (5 + 5w)) = 6w + -9 (-15 + -15w + (5 * 2w + 5w * 2w)) = 6w + -9 (-15 + -15w + (10w + 10w2)) = 6w + -9 Combine like terms: -15w + 10w = -5w (-15 + -5w + 10w2) = 6w + -9 Reorder the terms: -15 + -5w + 10w2 = -9 + 6w Solving -15 + -5w + 10w2 = -9 + 6w Solving for variable 'w'. Reorder the terms: -15 + 9 + -5w + -6w + 10w2 = -9 + 6w + 9 + -6w Combine like terms: -15 + 9 = -6 -6 + -5w + -6w + 10w2 = -9 + 6w + 9 + -6w Combine like terms: -5w + -6w = -11w -6 + -11w + 10w2 = -9 + 6w + 9 + -6w Reorder the terms: -6 + -11w + 10w2 = -9 + 9 + 6w + -6w Combine like terms: -9 + 9 = 0 -6 + -11w + 10w2 = 0 + 6w + -6w -6 + -11w + 10w2 = 6w + -6w Combine like terms: 6w + -6w = 0 -6 + -11w + 10w2 = 0 Factor a trinomial. (-2 + -5w)(3 + -2w) = 0Subproblem 1
Set the factor '(-2 + -5w)' equal to zero and attempt to solve: Simplifying -2 + -5w = 0 Solving -2 + -5w = 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 + -5w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5w = 0 + 2 -5w = 0 + 2 Combine like terms: 0 + 2 = 2 -5w = 2 Divide each side by '-5'. w = -0.4 Simplifying w = -0.4Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {-0.4, 1.5}
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