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Simplifying 7(6n + 32) + 8(n + 1) = 0 Reorder the terms: 7(32 + 6n) + 8(n + 1) = 0 (32 * 7 + 6n * 7) + 8(n + 1) = 0 (224 + 42n) + 8(n + 1) = 0 Reorder the terms: 224 + 42n + 8(1 + n) = 0 224 + 42n + (1 * 8 + n * 8) = 0 224 + 42n + (8 + 8n) = 0 Reorder the terms: 224 + 8 + 42n + 8n = 0 Combine like terms: 224 + 8 = 232 232 + 42n + 8n = 0 Combine like terms: 42n + 8n = 50n 232 + 50n = 0 Solving 232 + 50n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-232' to each side of the equation. 232 + -232 + 50n = 0 + -232 Combine like terms: 232 + -232 = 0 0 + 50n = 0 + -232 50n = 0 + -232 Combine like terms: 0 + -232 = -232 50n = -232 Divide each side by '50'. n = -4.64 Simplifying n = -4.64
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