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Simplifying ((n + 9) + -1n)((n + 9) + n) = ((n + 7) + -1n)((n + 7) + n) + 64 Reorder the terms: ((9 + n) + -1n)((n + 9) + n) = ((n + 7) + -1n)((n + 7) + n) + 64 Remove parenthesis around (9 + n) (9 + n + -1n)((n + 9) + n) = ((n + 7) + -1n)((n + 7) + n) + 64 Combine like terms: n + -1n = 0 (9 + 0)((n + 9) + n) = ((n + 7) + -1n)((n + 7) + n) + 64 (9)((n + 9) + n) = ((n + 7) + -1n)((n + 7) + n) + 64 Reorder the terms: 9((9 + n) + n) = ((n + 7) + -1n)((n + 7) + n) + 64 Remove parenthesis around (9 + n) 9(9 + n + n) = ((n + 7) + -1n)((n + 7) + n) + 64 Combine like terms: n + n = 2n 9(9 + 2n) = ((n + 7) + -1n)((n + 7) + n) + 64 (9 * 9 + 2n * 9) = ((n + 7) + -1n)((n + 7) + n) + 64 (81 + 18n) = ((n + 7) + -1n)((n + 7) + n) + 64 Reorder the terms: 81 + 18n = ((7 + n) + -1n)((n + 7) + n) + 64 Remove parenthesis around (7 + n) 81 + 18n = (7 + n + -1n)((n + 7) + n) + 64 Combine like terms: n + -1n = 0 81 + 18n = (7 + 0)((n + 7) + n) + 64 81 + 18n = (7)((n + 7) + n) + 64 Reorder the terms: 81 + 18n = 7((7 + n) + n) + 64 Remove parenthesis around (7 + n) 81 + 18n = 7(7 + n + n) + 64 Combine like terms: n + n = 2n 81 + 18n = 7(7 + 2n) + 64 81 + 18n = (7 * 7 + 2n * 7) + 64 81 + 18n = (49 + 14n) + 64 Reorder the terms: 81 + 18n = 49 + 64 + 14n Combine like terms: 49 + 64 = 113 81 + 18n = 113 + 14n Solving 81 + 18n = 113 + 14n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-14n' to each side of the equation. 81 + 18n + -14n = 113 + 14n + -14n Combine like terms: 18n + -14n = 4n 81 + 4n = 113 + 14n + -14n Combine like terms: 14n + -14n = 0 81 + 4n = 113 + 0 81 + 4n = 113 Add '-81' to each side of the equation. 81 + -81 + 4n = 113 + -81 Combine like terms: 81 + -81 = 0 0 + 4n = 113 + -81 4n = 113 + -81 Combine like terms: 113 + -81 = 32 4n = 32 Divide each side by '4'. n = 8 Simplifying n = 8
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