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Simplifying (w)(w + 4) + 15 = (w + 3)(w + 5) Reorder the terms: w(4 + w) + 15 = (w + 3)(w + 5) (4 * w + w * w) + 15 = (w + 3)(w + 5) (4w + w2) + 15 = (w + 3)(w + 5) Reorder the terms: 15 + 4w + w2 = (w + 3)(w + 5) Reorder the terms: 15 + 4w + w2 = (3 + w)(w + 5) Reorder the terms: 15 + 4w + w2 = (3 + w)(5 + w) Multiply (3 + w) * (5 + w) 15 + 4w + w2 = (3(5 + w) + w(5 + w)) 15 + 4w + w2 = ((5 * 3 + w * 3) + w(5 + w)) 15 + 4w + w2 = ((15 + 3w) + w(5 + w)) 15 + 4w + w2 = (15 + 3w + (5 * w + w * w)) 15 + 4w + w2 = (15 + 3w + (5w + w2)) Combine like terms: 3w + 5w = 8w 15 + 4w + w2 = (15 + 8w + w2) Add '-15' to each side of the equation. 15 + 4w + -15 + w2 = 15 + 8w + -15 + w2 Reorder the terms: 15 + -15 + 4w + w2 = 15 + 8w + -15 + w2 Combine like terms: 15 + -15 = 0 0 + 4w + w2 = 15 + 8w + -15 + w2 4w + w2 = 15 + 8w + -15 + w2 Reorder the terms: 4w + w2 = 15 + -15 + 8w + w2 Combine like terms: 15 + -15 = 0 4w + w2 = 0 + 8w + w2 4w + w2 = 8w + w2 Add '-1w2' to each side of the equation. 4w + w2 + -1w2 = 8w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 4w + 0 = 8w + w2 + -1w2 4w = 8w + w2 + -1w2 Combine like terms: w2 + -1w2 = 0 4w = 8w + 0 4w = 8w Solving 4w = 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. 4w + -8w = 8w + -8w Combine like terms: 4w + -8w = -4w -4w = 8w + -8w Combine like terms: 8w + -8w = 0 -4w = 0 Divide each side by '-4'. w = 0 Simplifying w = 0
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