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Simplifying 6(5n + 2) + 6 = -7(5 + -5n) + -7 Reorder the terms: 6(2 + 5n) + 6 = -7(5 + -5n) + -7 (2 * 6 + 5n * 6) + 6 = -7(5 + -5n) + -7 (12 + 30n) + 6 = -7(5 + -5n) + -7 Reorder the terms: 12 + 6 + 30n = -7(5 + -5n) + -7 Combine like terms: 12 + 6 = 18 18 + 30n = -7(5 + -5n) + -7 18 + 30n = (5 * -7 + -5n * -7) + -7 18 + 30n = (-35 + 35n) + -7 Reorder the terms: 18 + 30n = -35 + -7 + 35n Combine like terms: -35 + -7 = -42 18 + 30n = -42 + 35n Solving 18 + 30n = -42 + 35n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-35n' to each side of the equation. 18 + 30n + -35n = -42 + 35n + -35n Combine like terms: 30n + -35n = -5n 18 + -5n = -42 + 35n + -35n Combine like terms: 35n + -35n = 0 18 + -5n = -42 + 0 18 + -5n = -42 Add '-18' to each side of the equation. 18 + -18 + -5n = -42 + -18 Combine like terms: 18 + -18 = 0 0 + -5n = -42 + -18 -5n = -42 + -18 Combine like terms: -42 + -18 = -60 -5n = -60 Divide each side by '-5'. n = 12 Simplifying n = 12
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