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Simplifying 5 = -2(w + 2)(w + 5) + -5(w + 2) Reorder the terms: 5 = -2(2 + w)(w + 5) + -5(w + 2) Reorder the terms: 5 = -2(2 + w)(5 + w) + -5(w + 2) Multiply (2 + w) * (5 + w) 5 = -2(2(5 + w) + w(5 + w)) + -5(w + 2) 5 = -2((5 * 2 + w * 2) + w(5 + w)) + -5(w + 2) 5 = -2((10 + 2w) + w(5 + w)) + -5(w + 2) 5 = -2(10 + 2w + (5 * w + w * w)) + -5(w + 2) 5 = -2(10 + 2w + (5w + w2)) + -5(w + 2) Combine like terms: 2w + 5w = 7w 5 = -2(10 + 7w + w2) + -5(w + 2) 5 = (10 * -2 + 7w * -2 + w2 * -2) + -5(w + 2) 5 = (-20 + -14w + -2w2) + -5(w + 2) Reorder the terms: 5 = -20 + -14w + -2w2 + -5(2 + w) 5 = -20 + -14w + -2w2 + (2 * -5 + w * -5) 5 = -20 + -14w + -2w2 + (-10 + -5w) Reorder the terms: 5 = -20 + -10 + -14w + -5w + -2w2 Combine like terms: -20 + -10 = -30 5 = -30 + -14w + -5w + -2w2 Combine like terms: -14w + -5w = -19w 5 = -30 + -19w + -2w2 Solving 5 = -30 + -19w + -2w2 Solving for variable 'w'. Combine like terms: 5 + 30 = 35 35 + 19w + 2w2 = -30 + -19w + -2w2 + 30 + 19w + 2w2 Reorder the terms: 35 + 19w + 2w2 = -30 + 30 + -19w + 19w + -2w2 + 2w2 Combine like terms: -30 + 30 = 0 35 + 19w + 2w2 = 0 + -19w + 19w + -2w2 + 2w2 35 + 19w + 2w2 = -19w + 19w + -2w2 + 2w2 Combine like terms: -19w + 19w = 0 35 + 19w + 2w2 = 0 + -2w2 + 2w2 35 + 19w + 2w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 35 + 19w + 2w2 = 0 Factor a trinomial. (7 + w)(5 + 2w) = 0Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Subproblem 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 = {-7, -2.5}
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