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Simplifying 7(n + 5) + 8(n + 7) = 0 Reorder the terms: 7(5 + n) + 8(n + 7) = 0 (5 * 7 + n * 7) + 8(n + 7) = 0 (35 + 7n) + 8(n + 7) = 0 Reorder the terms: 35 + 7n + 8(7 + n) = 0 35 + 7n + (7 * 8 + n * 8) = 0 35 + 7n + (56 + 8n) = 0 Reorder the terms: 35 + 56 + 7n + 8n = 0 Combine like terms: 35 + 56 = 91 91 + 7n + 8n = 0 Combine like terms: 7n + 8n = 15n 91 + 15n = 0 Solving 91 + 15n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-91' to each side of the equation. 91 + -91 + 15n = 0 + -91 Combine like terms: 91 + -91 = 0 0 + 15n = 0 + -91 15n = 0 + -91 Combine like terms: 0 + -91 = -91 15n = -91 Divide each side by '15'. n = -6.066666667 Simplifying n = -6.066666667
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