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Simplifying 2(7 + -5(1 + -1n)) + 2n = -12 + 3(6(n + 1) + -3n) 2(7 + (1 * -5 + -1n * -5)) + 2n = -12 + 3(6(n + 1) + -3n) 2(7 + (-5 + 5n)) + 2n = -12 + 3(6(n + 1) + -3n) Combine like terms: 7 + -5 = 2 2(2 + 5n) + 2n = -12 + 3(6(n + 1) + -3n) (2 * 2 + 5n * 2) + 2n = -12 + 3(6(n + 1) + -3n) (4 + 10n) + 2n = -12 + 3(6(n + 1) + -3n) Combine like terms: 10n + 2n = 12n 4 + 12n = -12 + 3(6(n + 1) + -3n) Reorder the terms: 4 + 12n = -12 + 3(6(1 + n) + -3n) 4 + 12n = -12 + 3((1 * 6 + n * 6) + -3n) 4 + 12n = -12 + 3((6 + 6n) + -3n) Combine like terms: 6n + -3n = 3n 4 + 12n = -12 + 3(6 + 3n) 4 + 12n = -12 + (6 * 3 + 3n * 3) 4 + 12n = -12 + (18 + 9n) Combine like terms: -12 + 18 = 6 4 + 12n = 6 + 9n Solving 4 + 12n = 6 + 9n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9n' to each side of the equation. 4 + 12n + -9n = 6 + 9n + -9n Combine like terms: 12n + -9n = 3n 4 + 3n = 6 + 9n + -9n Combine like terms: 9n + -9n = 0 4 + 3n = 6 + 0 4 + 3n = 6 Add '-4' to each side of the equation. 4 + -4 + 3n = 6 + -4 Combine like terms: 4 + -4 = 0 0 + 3n = 6 + -4 3n = 6 + -4 Combine like terms: 6 + -4 = 2 3n = 2 Divide each side by '3'. n = 0.6666666667 Simplifying n = 0.6666666667
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