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Simplifying 2(7 + -6(1 + -1n)) + 9n = -32(6(n + 1) + -3n) 2(7 + (1 * -6 + -1n * -6)) + 9n = -32(6(n + 1) + -3n) 2(7 + (-6 + 6n)) + 9n = -32(6(n + 1) + -3n) Combine like terms: 7 + -6 = 1 2(1 + 6n) + 9n = -32(6(n + 1) + -3n) (1 * 2 + 6n * 2) + 9n = -32(6(n + 1) + -3n) (2 + 12n) + 9n = -32(6(n + 1) + -3n) Combine like terms: 12n + 9n = 21n 2 + 21n = -32(6(n + 1) + -3n) Reorder the terms: 2 + 21n = -32(6(1 + n) + -3n) 2 + 21n = -32((1 * 6 + n * 6) + -3n) 2 + 21n = -32((6 + 6n) + -3n) Combine like terms: 6n + -3n = 3n 2 + 21n = -32(6 + 3n) 2 + 21n = (6 * -32 + 3n * -32) 2 + 21n = (-192 + -96n) Solving 2 + 21n = -192 + -96n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '96n' to each side of the equation. 2 + 21n + 96n = -192 + -96n + 96n Combine like terms: 21n + 96n = 117n 2 + 117n = -192 + -96n + 96n Combine like terms: -96n + 96n = 0 2 + 117n = -192 + 0 2 + 117n = -192 Add '-2' to each side of the equation. 2 + -2 + 117n = -192 + -2 Combine like terms: 2 + -2 = 0 0 + 117n = -192 + -2 117n = -192 + -2 Combine like terms: -192 + -2 = -194 117n = -194 Divide each side by '117'. n = -1.658119658 Simplifying n = -1.658119658
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