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Simplifying w(w + 6) + 48 = (w + 1)(w + 7) Reorder the terms: w(6 + w) + 48 = (w + 1)(w + 7) (6 * w + w * w) + 48 = (w + 1)(w + 7) (6w + w2) + 48 = (w + 1)(w + 7) Reorder the terms: 48 + 6w + w2 = (w + 1)(w + 7) Reorder the terms: 48 + 6w + w2 = (1 + w)(w + 7) Reorder the terms: 48 + 6w + w2 = (1 + w)(7 + w) Multiply (1 + w) * (7 + w) 48 + 6w + w2 = (1(7 + w) + w(7 + w)) 48 + 6w + w2 = ((7 * 1 + w * 1) + w(7 + w)) 48 + 6w + w2 = ((7 + 1w) + w(7 + w)) 48 + 6w + w2 = (7 + 1w + (7 * w + w * w)) 48 + 6w + w2 = (7 + 1w + (7w + w2)) Combine like terms: 1w + 7w = 8w 48 + 6w + w2 = (7 + 8w + w2) Add '-1w2' to each side of the equation. 48 + 6w + w2 + -1w2 = 7 + 8w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 48 + 6w + 0 = 7 + 8w + w2 + -1w2 48 + 6w = 7 + 8w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 48 + 6w = 7 + 8w + 0 48 + 6w = 7 + 8w Solving 48 + 6w = 7 + 8w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8w' to each side of the equation. 48 + 6w + -8w = 7 + 8w + -8w Combine like terms: 6w + -8w = -2w 48 + -2w = 7 + 8w + -8w Combine like terms: 8w + -8w = 0 48 + -2w = 7 + 0 48 + -2w = 7 Add '-48' to each side of the equation. 48 + -48 + -2w = 7 + -48 Combine like terms: 48 + -48 = 0 0 + -2w = 7 + -48 -2w = 7 + -48 Combine like terms: 7 + -48 = -41 -2w = -41 Divide each side by '-2'. w = 20.5 Simplifying w = 20.5
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