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Simplifying 5(8n + 30) + 8(n + 1) = 0 Reorder the terms: 5(30 + 8n) + 8(n + 1) = 0 (30 * 5 + 8n * 5) + 8(n + 1) = 0 (150 + 40n) + 8(n + 1) = 0 Reorder the terms: 150 + 40n + 8(1 + n) = 0 150 + 40n + (1 * 8 + n * 8) = 0 150 + 40n + (8 + 8n) = 0 Reorder the terms: 150 + 8 + 40n + 8n = 0 Combine like terms: 150 + 8 = 158 158 + 40n + 8n = 0 Combine like terms: 40n + 8n = 48n 158 + 48n = 0 Solving 158 + 48n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-158' to each side of the equation. 158 + -158 + 48n = 0 + -158 Combine like terms: 158 + -158 = 0 0 + 48n = 0 + -158 48n = 0 + -158 Combine like terms: 0 + -158 = -158 48n = -158 Divide each side by '48'. n = -3.291666667 Simplifying n = -3.291666667
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