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Simplifying (y + 2)(y + 7) = y2 + 32 Reorder the terms: (2 + y)(y + 7) = y2 + 32 Reorder the terms: (2 + y)(7 + y) = y2 + 32 Multiply (2 + y) * (7 + y) (2(7 + y) + y(7 + y)) = y2 + 32 ((7 * 2 + y * 2) + y(7 + y)) = y2 + 32 ((14 + 2y) + y(7 + y)) = y2 + 32 (14 + 2y + (7 * y + y * y)) = y2 + 32 (14 + 2y + (7y + y2)) = y2 + 32 Combine like terms: 2y + 7y = 9y (14 + 9y + y2) = y2 + 32 Reorder the terms: 14 + 9y + y2 = 32 + y2 Add '-1y2' to each side of the equation. 14 + 9y + y2 + -1y2 = 32 + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 14 + 9y + 0 = 32 + y2 + -1y2 14 + 9y = 32 + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 14 + 9y = 32 + 0 14 + 9y = 32 Solving 14 + 9y = 32 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 9y = 32 + -14 Combine like terms: 14 + -14 = 0 0 + 9y = 32 + -14 9y = 32 + -14 Combine like terms: 32 + -14 = 18 9y = 18 Divide each side by '9'. y = 2 Simplifying y = 2
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