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Simplifying (w + 12)(w + 4) + -1w(w + 8) = 216 Reorder the terms: (12 + w)(w + 4) + -1w(w + 8) = 216 Reorder the terms: (12 + w)(4 + w) + -1w(w + 8) = 216 Multiply (12 + w) * (4 + w) (12(4 + w) + w(4 + w)) + -1w(w + 8) = 216 ((4 * 12 + w * 12) + w(4 + w)) + -1w(w + 8) = 216 ((48 + 12w) + w(4 + w)) + -1w(w + 8) = 216 (48 + 12w + (4 * w + w * w)) + -1w(w + 8) = 216 (48 + 12w + (4w + w2)) + -1w(w + 8) = 216 Combine like terms: 12w + 4w = 16w (48 + 16w + w2) + -1w(w + 8) = 216 Reorder the terms: 48 + 16w + w2 + -1w(8 + w) = 216 48 + 16w + w2 + (8 * -1w + w * -1w) = 216 48 + 16w + w2 + (-8w + -1w2) = 216 Reorder the terms: 48 + 16w + -8w + w2 + -1w2 = 216 Combine like terms: 16w + -8w = 8w 48 + 8w + w2 + -1w2 = 216 Combine like terms: w2 + -1w2 = 0 48 + 8w + 0 = 216 48 + 8w = 216 Solving 48 + 8w = 216 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + 8w = 216 + -48 Combine like terms: 48 + -48 = 0 0 + 8w = 216 + -48 8w = 216 + -48 Combine like terms: 216 + -48 = 168 8w = 168 Divide each side by '8'. w = 21 Simplifying w = 21
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