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Simplifying 32 = 7(n + 7) + 5(5n + 3) Reorder the terms: 32 = 7(7 + n) + 5(5n + 3) 32 = (7 * 7 + n * 7) + 5(5n + 3) 32 = (49 + 7n) + 5(5n + 3) Reorder the terms: 32 = 49 + 7n + 5(3 + 5n) 32 = 49 + 7n + (3 * 5 + 5n * 5) 32 = 49 + 7n + (15 + 25n) Reorder the terms: 32 = 49 + 15 + 7n + 25n Combine like terms: 49 + 15 = 64 32 = 64 + 7n + 25n Combine like terms: 7n + 25n = 32n 32 = 64 + 32n Solving 32 = 64 + 32n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-32n' to each side of the equation. 32 + -32n = 64 + 32n + -32n Combine like terms: 32n + -32n = 0 32 + -32n = 64 + 0 32 + -32n = 64 Add '-32' to each side of the equation. 32 + -32 + -32n = 64 + -32 Combine like terms: 32 + -32 = 0 0 + -32n = 64 + -32 -32n = 64 + -32 Combine like terms: 64 + -32 = 32 -32n = 32 Divide each side by '-32'. n = -1 Simplifying n = -1
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