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Simplifying 4(2n + 3) + -5(3n + 2) = 9 Reorder the terms: 4(3 + 2n) + -5(3n + 2) = 9 (3 * 4 + 2n * 4) + -5(3n + 2) = 9 (12 + 8n) + -5(3n + 2) = 9 Reorder the terms: 12 + 8n + -5(2 + 3n) = 9 12 + 8n + (2 * -5 + 3n * -5) = 9 12 + 8n + (-10 + -15n) = 9 Reorder the terms: 12 + -10 + 8n + -15n = 9 Combine like terms: 12 + -10 = 2 2 + 8n + -15n = 9 Combine like terms: 8n + -15n = -7n 2 + -7n = 9 Solving 2 + -7n = 9 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7n = 9 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 9 + -2 -7n = 9 + -2 Combine like terms: 9 + -2 = 7 -7n = 7 Divide each side by '-7'. n = -1 Simplifying n = -1
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