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Simplifying (w + 4)(w + 9) + -1(w)(w + 5) = 76 Reorder the terms: (4 + w)(w + 9) + -1(w)(w + 5) = 76 Reorder the terms: (4 + w)(9 + w) + -1(w)(w + 5) = 76 Multiply (4 + w) * (9 + w) (4(9 + w) + w(9 + w)) + -1(w)(w + 5) = 76 ((9 * 4 + w * 4) + w(9 + w)) + -1(w)(w + 5) = 76 ((36 + 4w) + w(9 + w)) + -1(w)(w + 5) = 76 (36 + 4w + (9 * w + w * w)) + -1(w)(w + 5) = 76 (36 + 4w + (9w + w2)) + -1(w)(w + 5) = 76 Combine like terms: 4w + 9w = 13w (36 + 13w + w2) + -1(w)(w + 5) = 76 Reorder the terms: 36 + 13w + w2 + -1w(5 + w) = 76 36 + 13w + w2 + (5 * -1w + w * -1w) = 76 36 + 13w + w2 + (-5w + -1w2) = 76 Reorder the terms: 36 + 13w + -5w + w2 + -1w2 = 76 Combine like terms: 13w + -5w = 8w 36 + 8w + w2 + -1w2 = 76 Combine like terms: w2 + -1w2 = 0 36 + 8w + 0 = 76 36 + 8w = 76 Solving 36 + 8w = 76 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + 8w = 76 + -36 Combine like terms: 36 + -36 = 0 0 + 8w = 76 + -36 8w = 76 + -36 Combine like terms: 76 + -36 = 40 8w = 40 Divide each side by '8'. w = 5 Simplifying w = 5
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