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Simplifying 3(12n + -2) + 8(3 + -3n) = n + 5 + -9 Reorder the terms: 3(-2 + 12n) + 8(3 + -3n) = n + 5 + -9 (-2 * 3 + 12n * 3) + 8(3 + -3n) = n + 5 + -9 (-6 + 36n) + 8(3 + -3n) = n + 5 + -9 -6 + 36n + (3 * 8 + -3n * 8) = n + 5 + -9 -6 + 36n + (24 + -24n) = n + 5 + -9 Reorder the terms: -6 + 24 + 36n + -24n = n + 5 + -9 Combine like terms: -6 + 24 = 18 18 + 36n + -24n = n + 5 + -9 Combine like terms: 36n + -24n = 12n 18 + 12n = n + 5 + -9 Reorder the terms: 18 + 12n = 5 + -9 + n Combine like terms: 5 + -9 = -4 18 + 12n = -4 + n Solving 18 + 12n = -4 + n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1n' to each side of the equation. 18 + 12n + -1n = -4 + n + -1n Combine like terms: 12n + -1n = 11n 18 + 11n = -4 + n + -1n Combine like terms: n + -1n = 0 18 + 11n = -4 + 0 18 + 11n = -4 Add '-18' to each side of the equation. 18 + -18 + 11n = -4 + -18 Combine like terms: 18 + -18 = 0 0 + 11n = -4 + -18 11n = -4 + -18 Combine like terms: -4 + -18 = -22 11n = -22 Divide each side by '11'. n = -2 Simplifying n = -2
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