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Simplifying 5(3n + 34) + 6(n + 1) = 0 Reorder the terms: 5(34 + 3n) + 6(n + 1) = 0 (34 * 5 + 3n * 5) + 6(n + 1) = 0 (170 + 15n) + 6(n + 1) = 0 Reorder the terms: 170 + 15n + 6(1 + n) = 0 170 + 15n + (1 * 6 + n * 6) = 0 170 + 15n + (6 + 6n) = 0 Reorder the terms: 170 + 6 + 15n + 6n = 0 Combine like terms: 170 + 6 = 176 176 + 15n + 6n = 0 Combine like terms: 15n + 6n = 21n 176 + 21n = 0 Solving 176 + 21n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-176' to each side of the equation. 176 + -176 + 21n = 0 + -176 Combine like terms: 176 + -176 = 0 0 + 21n = 0 + -176 21n = 0 + -176 Combine like terms: 0 + -176 = -176 21n = -176 Divide each side by '21'. n = -8.380952381 Simplifying n = -8.380952381
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