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Simplifying (w + 4)(2w + 4) + -1w(2w) = 196 Reorder the terms: (4 + w)(2w + 4) + -1w(2w) = 196 Reorder the terms: (4 + w)(4 + 2w) + -1w(2w) = 196 Multiply (4 + w) * (4 + 2w) (4(4 + 2w) + w(4 + 2w)) + -1w(2w) = 196 ((4 * 4 + 2w * 4) + w(4 + 2w)) + -1w(2w) = 196 ((16 + 8w) + w(4 + 2w)) + -1w(2w) = 196 (16 + 8w + (4 * w + 2w * w)) + -1w(2w) = 196 (16 + 8w + (4w + 2w2)) + -1w(2w) = 196 Combine like terms: 8w + 4w = 12w (16 + 12w + 2w2) + -1w(2w) = 196 Remove parenthesis around (2w) 16 + 12w + 2w2 + -1w * 2w = 196 Reorder the terms for easier multiplication: 16 + 12w + 2w2 + -1 * 2w * w = 196 Multiply -1 * 2 16 + 12w + 2w2 + -2w * w = 196 Multiply w * w 16 + 12w + 2w2 + -2w2 = 196 Combine like terms: 2w2 + -2w2 = 0 16 + 12w + 0 = 196 16 + 12w = 196 Solving 16 + 12w = 196 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 12w = 196 + -16 Combine like terms: 16 + -16 = 0 0 + 12w = 196 + -16 12w = 196 + -16 Combine like terms: 196 + -16 = 180 12w = 180 Divide each side by '12'. w = 15 Simplifying w = 15
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