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Simplifying w(w + 3) + 26 = (w + 2)(w + 5) Reorder the terms: w(3 + w) + 26 = (w + 2)(w + 5) (3 * w + w * w) + 26 = (w + 2)(w + 5) (3w + w2) + 26 = (w + 2)(w + 5) Reorder the terms: 26 + 3w + w2 = (w + 2)(w + 5) Reorder the terms: 26 + 3w + w2 = (2 + w)(w + 5) Reorder the terms: 26 + 3w + w2 = (2 + w)(5 + w) Multiply (2 + w) * (5 + w) 26 + 3w + w2 = (2(5 + w) + w(5 + w)) 26 + 3w + w2 = ((5 * 2 + w * 2) + w(5 + w)) 26 + 3w + w2 = ((10 + 2w) + w(5 + w)) 26 + 3w + w2 = (10 + 2w + (5 * w + w * w)) 26 + 3w + w2 = (10 + 2w + (5w + w2)) Combine like terms: 2w + 5w = 7w 26 + 3w + w2 = (10 + 7w + w2) Add '-1w2' to each side of the equation. 26 + 3w + w2 + -1w2 = 10 + 7w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 26 + 3w + 0 = 10 + 7w + w2 + -1w2 26 + 3w = 10 + 7w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 26 + 3w = 10 + 7w + 0 26 + 3w = 10 + 7w Solving 26 + 3w = 10 + 7w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7w' to each side of the equation. 26 + 3w + -7w = 10 + 7w + -7w Combine like terms: 3w + -7w = -4w 26 + -4w = 10 + 7w + -7w Combine like terms: 7w + -7w = 0 26 + -4w = 10 + 0 26 + -4w = 10 Add '-26' to each side of the equation. 26 + -26 + -4w = 10 + -26 Combine like terms: 26 + -26 = 0 0 + -4w = 10 + -26 -4w = 10 + -26 Combine like terms: 10 + -26 = -16 -4w = -16 Divide each side by '-4'. w = 4 Simplifying w = 4
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