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Simplifying (y + -5)(y + -8) = y2 + 1 Reorder the terms: (-5 + y)(y + -8) = y2 + 1 Reorder the terms: (-5 + y)(-8 + y) = y2 + 1 Multiply (-5 + y) * (-8 + y) (-5(-8 + y) + y(-8 + y)) = y2 + 1 ((-8 * -5 + y * -5) + y(-8 + y)) = y2 + 1 ((40 + -5y) + y(-8 + y)) = y2 + 1 (40 + -5y + (-8 * y + y * y)) = y2 + 1 (40 + -5y + (-8y + y2)) = y2 + 1 Combine like terms: -5y + -8y = -13y (40 + -13y + y2) = y2 + 1 Reorder the terms: 40 + -13y + y2 = 1 + y2 Add '-1y2' to each side of the equation. 40 + -13y + y2 + -1y2 = 1 + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 40 + -13y + 0 = 1 + y2 + -1y2 40 + -13y = 1 + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 40 + -13y = 1 + 0 40 + -13y = 1 Solving 40 + -13y = 1 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -13y = 1 + -40 Combine like terms: 40 + -40 = 0 0 + -13y = 1 + -40 -13y = 1 + -40 Combine like terms: 1 + -40 = -39 -13y = -39 Divide each side by '-13'. y = 3 Simplifying y = 3
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