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Simplifying (n + 7)(n + 2) + -1n(n + 5) = 66 Reorder the terms: (7 + n)(n + 2) + -1n(n + 5) = 66 Reorder the terms: (7 + n)(2 + n) + -1n(n + 5) = 66 Multiply (7 + n) * (2 + n) (7(2 + n) + n(2 + n)) + -1n(n + 5) = 66 ((2 * 7 + n * 7) + n(2 + n)) + -1n(n + 5) = 66 ((14 + 7n) + n(2 + n)) + -1n(n + 5) = 66 (14 + 7n + (2 * n + n * n)) + -1n(n + 5) = 66 (14 + 7n + (2n + n2)) + -1n(n + 5) = 66 Combine like terms: 7n + 2n = 9n (14 + 9n + n2) + -1n(n + 5) = 66 Reorder the terms: 14 + 9n + n2 + -1n(5 + n) = 66 14 + 9n + n2 + (5 * -1n + n * -1n) = 66 14 + 9n + n2 + (-5n + -1n2) = 66 Reorder the terms: 14 + 9n + -5n + n2 + -1n2 = 66 Combine like terms: 9n + -5n = 4n 14 + 4n + n2 + -1n2 = 66 Combine like terms: n2 + -1n2 = 0 14 + 4n + 0 = 66 14 + 4n = 66 Solving 14 + 4n = 66 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 4n = 66 + -14 Combine like terms: 14 + -14 = 0 0 + 4n = 66 + -14 4n = 66 + -14 Combine like terms: 66 + -14 = 52 4n = 52 Divide each side by '4'. n = 13 Simplifying n = 13
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