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Simplifying 12n + -7(n + 12) = 2(5n + 6) + 9 Reorder the terms: 12n + -7(12 + n) = 2(5n + 6) + 9 12n + (12 * -7 + n * -7) = 2(5n + 6) + 9 12n + (-84 + -7n) = 2(5n + 6) + 9 Reorder the terms: -84 + 12n + -7n = 2(5n + 6) + 9 Combine like terms: 12n + -7n = 5n -84 + 5n = 2(5n + 6) + 9 Reorder the terms: -84 + 5n = 2(6 + 5n) + 9 -84 + 5n = (6 * 2 + 5n * 2) + 9 -84 + 5n = (12 + 10n) + 9 Reorder the terms: -84 + 5n = 12 + 9 + 10n Combine like terms: 12 + 9 = 21 -84 + 5n = 21 + 10n Solving -84 + 5n = 21 + 10n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10n' to each side of the equation. -84 + 5n + -10n = 21 + 10n + -10n Combine like terms: 5n + -10n = -5n -84 + -5n = 21 + 10n + -10n Combine like terms: 10n + -10n = 0 -84 + -5n = 21 + 0 -84 + -5n = 21 Add '84' to each side of the equation. -84 + 84 + -5n = 21 + 84 Combine like terms: -84 + 84 = 0 0 + -5n = 21 + 84 -5n = 21 + 84 Combine like terms: 21 + 84 = 105 -5n = 105 Divide each side by '-5'. n = -21 Simplifying n = -21
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