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Simplifying 6(3n + 2) = 7(7n + 6) + 6 Reorder the terms: 6(2 + 3n) = 7(7n + 6) + 6 (2 * 6 + 3n * 6) = 7(7n + 6) + 6 (12 + 18n) = 7(7n + 6) + 6 Reorder the terms: 12 + 18n = 7(6 + 7n) + 6 12 + 18n = (6 * 7 + 7n * 7) + 6 12 + 18n = (42 + 49n) + 6 Reorder the terms: 12 + 18n = 42 + 6 + 49n Combine like terms: 42 + 6 = 48 12 + 18n = 48 + 49n Solving 12 + 18n = 48 + 49n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-49n' to each side of the equation. 12 + 18n + -49n = 48 + 49n + -49n Combine like terms: 18n + -49n = -31n 12 + -31n = 48 + 49n + -49n Combine like terms: 49n + -49n = 0 12 + -31n = 48 + 0 12 + -31n = 48 Add '-12' to each side of the equation. 12 + -12 + -31n = 48 + -12 Combine like terms: 12 + -12 = 0 0 + -31n = 48 + -12 -31n = 48 + -12 Combine like terms: 48 + -12 = 36 -31n = 36 Divide each side by '-31'. n = -1.161290323 Simplifying n = -1.161290323
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