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Simplifying 4(2n + 6) + 3(n + 12) + 3(3n + -4) = 0 Reorder the terms: 4(6 + 2n) + 3(n + 12) + 3(3n + -4) = 0 (6 * 4 + 2n * 4) + 3(n + 12) + 3(3n + -4) = 0 (24 + 8n) + 3(n + 12) + 3(3n + -4) = 0 Reorder the terms: 24 + 8n + 3(12 + n) + 3(3n + -4) = 0 24 + 8n + (12 * 3 + n * 3) + 3(3n + -4) = 0 24 + 8n + (36 + 3n) + 3(3n + -4) = 0 Reorder the terms: 24 + 8n + 36 + 3n + 3(-4 + 3n) = 0 24 + 8n + 36 + 3n + (-4 * 3 + 3n * 3) = 0 24 + 8n + 36 + 3n + (-12 + 9n) = 0 Reorder the terms: 24 + 36 + -12 + 8n + 3n + 9n = 0 Combine like terms: 24 + 36 = 60 60 + -12 + 8n + 3n + 9n = 0 Combine like terms: 60 + -12 = 48 48 + 8n + 3n + 9n = 0 Combine like terms: 8n + 3n = 11n 48 + 11n + 9n = 0 Combine like terms: 11n + 9n = 20n 48 + 20n = 0 Solving 48 + 20n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + 20n = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 20n = 0 + -48 20n = 0 + -48 Combine like terms: 0 + -48 = -48 20n = -48 Divide each side by '20'. n = -2.4 Simplifying n = -2.4
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