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Simplifying 12(n + 4) + 6 = 6(n + 7) + -42 Reorder the terms: 12(4 + n) + 6 = 6(n + 7) + -42 (4 * 12 + n * 12) + 6 = 6(n + 7) + -42 (48 + 12n) + 6 = 6(n + 7) + -42 Reorder the terms: 48 + 6 + 12n = 6(n + 7) + -42 Combine like terms: 48 + 6 = 54 54 + 12n = 6(n + 7) + -42 Reorder the terms: 54 + 12n = 6(7 + n) + -42 54 + 12n = (7 * 6 + n * 6) + -42 54 + 12n = (42 + 6n) + -42 Reorder the terms: 54 + 12n = 42 + -42 + 6n Combine like terms: 42 + -42 = 0 54 + 12n = 0 + 6n 54 + 12n = 6n Solving 54 + 12n = 6n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6n' to each side of the equation. 54 + 12n + -6n = 6n + -6n Combine like terms: 12n + -6n = 6n 54 + 6n = 6n + -6n Combine like terms: 6n + -6n = 0 54 + 6n = 0 Add '-54' to each side of the equation. 54 + -54 + 6n = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 6n = 0 + -54 6n = 0 + -54 Combine like terms: 0 + -54 = -54 6n = -54 Divide each side by '6'. n = -9 Simplifying n = -9
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