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Simplifying 3n + -1(6 + -1n) + 2(5 + -6n) = 12 3n + (6 * -1 + -1n * -1) + 2(5 + -6n) = 12 3n + (-6 + 1n) + 2(5 + -6n) = 12 3n + -6 + 1n + (5 * 2 + -6n * 2) = 12 3n + -6 + 1n + (10 + -12n) = 12 Reorder the terms: -6 + 10 + 3n + 1n + -12n = 12 Combine like terms: -6 + 10 = 4 4 + 3n + 1n + -12n = 12 Combine like terms: 3n + 1n = 4n 4 + 4n + -12n = 12 Combine like terms: 4n + -12n = -8n 4 + -8n = 12 Solving 4 + -8n = 12 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -8n = 12 + -4 Combine like terms: 4 + -4 = 0 0 + -8n = 12 + -4 -8n = 12 + -4 Combine like terms: 12 + -4 = 8 -8n = 8 Divide each side by '-8'. n = -1 Simplifying n = -1
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