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Simplifying (n + -1)(n + 3) + -1(n + 5)(n + -2) = 5 Reorder the terms: (-1 + n)(n + 3) + -1(n + 5)(n + -2) = 5 Reorder the terms: (-1 + n)(3 + n) + -1(n + 5)(n + -2) = 5 Multiply (-1 + n) * (3 + n) (-1(3 + n) + n(3 + n)) + -1(n + 5)(n + -2) = 5 ((3 * -1 + n * -1) + n(3 + n)) + -1(n + 5)(n + -2) = 5 ((-3 + -1n) + n(3 + n)) + -1(n + 5)(n + -2) = 5 (-3 + -1n + (3 * n + n * n)) + -1(n + 5)(n + -2) = 5 (-3 + -1n + (3n + n2)) + -1(n + 5)(n + -2) = 5 Combine like terms: -1n + 3n = 2n (-3 + 2n + n2) + -1(n + 5)(n + -2) = 5 Reorder the terms: -3 + 2n + n2 + -1(5 + n)(n + -2) = 5 Reorder the terms: -3 + 2n + n2 + -1(5 + n)(-2 + n) = 5 Multiply (5 + n) * (-2 + n) -3 + 2n + n2 + -1(5(-2 + n) + n(-2 + n)) = 5 -3 + 2n + n2 + -1((-2 * 5 + n * 5) + n(-2 + n)) = 5 -3 + 2n + n2 + -1((-10 + 5n) + n(-2 + n)) = 5 -3 + 2n + n2 + -1(-10 + 5n + (-2 * n + n * n)) = 5 -3 + 2n + n2 + -1(-10 + 5n + (-2n + n2)) = 5 Combine like terms: 5n + -2n = 3n -3 + 2n + n2 + -1(-10 + 3n + n2) = 5 -3 + 2n + n2 + (-10 * -1 + 3n * -1 + n2 * -1) = 5 -3 + 2n + n2 + (10 + -3n + -1n2) = 5 Reorder the terms: -3 + 10 + 2n + -3n + n2 + -1n2 = 5 Combine like terms: -3 + 10 = 7 7 + 2n + -3n + n2 + -1n2 = 5 Combine like terms: 2n + -3n = -1n 7 + -1n + n2 + -1n2 = 5 Combine like terms: n2 + -1n2 = 0 7 + -1n + 0 = 5 7 + -1n = 5 Solving 7 + -1n = 5 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 5 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 5 + -7 -1n = 5 + -7 Combine like terms: 5 + -7 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2
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