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Simplifying 6(8n + 30) + 7(n + 1) = 0 Reorder the terms: 6(30 + 8n) + 7(n + 1) = 0 (30 * 6 + 8n * 6) + 7(n + 1) = 0 (180 + 48n) + 7(n + 1) = 0 Reorder the terms: 180 + 48n + 7(1 + n) = 0 180 + 48n + (1 * 7 + n * 7) = 0 180 + 48n + (7 + 7n) = 0 Reorder the terms: 180 + 7 + 48n + 7n = 0 Combine like terms: 180 + 7 = 187 187 + 48n + 7n = 0 Combine like terms: 48n + 7n = 55n 187 + 55n = 0 Solving 187 + 55n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-187' to each side of the equation. 187 + -187 + 55n = 0 + -187 Combine like terms: 187 + -187 = 0 0 + 55n = 0 + -187 55n = 0 + -187 Combine like terms: 0 + -187 = -187 55n = -187 Divide each side by '55'. n = -3.4 Simplifying n = -3.4
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