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Simplifying 3(6 + -1n) + 4(3n + 5) + 3(6 + -1n) = 4(3 + n) (6 * 3 + -1n * 3) + 4(3n + 5) + 3(6 + -1n) = 4(3 + n) (18 + -3n) + 4(3n + 5) + 3(6 + -1n) = 4(3 + n) Reorder the terms: 18 + -3n + 4(5 + 3n) + 3(6 + -1n) = 4(3 + n) 18 + -3n + (5 * 4 + 3n * 4) + 3(6 + -1n) = 4(3 + n) 18 + -3n + (20 + 12n) + 3(6 + -1n) = 4(3 + n) 18 + -3n + 20 + 12n + (6 * 3 + -1n * 3) = 4(3 + n) 18 + -3n + 20 + 12n + (18 + -3n) = 4(3 + n) Reorder the terms: 18 + 20 + 18 + -3n + 12n + -3n = 4(3 + n) Combine like terms: 18 + 20 = 38 38 + 18 + -3n + 12n + -3n = 4(3 + n) Combine like terms: 38 + 18 = 56 56 + -3n + 12n + -3n = 4(3 + n) Combine like terms: -3n + 12n = 9n 56 + 9n + -3n = 4(3 + n) Combine like terms: 9n + -3n = 6n 56 + 6n = 4(3 + n) 56 + 6n = (3 * 4 + n * 4) 56 + 6n = (12 + 4n) Solving 56 + 6n = 12 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. 56 + 6n + -4n = 12 + 4n + -4n Combine like terms: 6n + -4n = 2n 56 + 2n = 12 + 4n + -4n Combine like terms: 4n + -4n = 0 56 + 2n = 12 + 0 56 + 2n = 12 Add '-56' to each side of the equation. 56 + -56 + 2n = 12 + -56 Combine like terms: 56 + -56 = 0 0 + 2n = 12 + -56 2n = 12 + -56 Combine like terms: 12 + -56 = -44 2n = -44 Divide each side by '2'. n = -22 Simplifying n = -22
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