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Simplifying 6(3n + 2) = 9(5n + 2) + 7 Reorder the terms: 6(2 + 3n) = 9(5n + 2) + 7 (2 * 6 + 3n * 6) = 9(5n + 2) + 7 (12 + 18n) = 9(5n + 2) + 7 Reorder the terms: 12 + 18n = 9(2 + 5n) + 7 12 + 18n = (2 * 9 + 5n * 9) + 7 12 + 18n = (18 + 45n) + 7 Reorder the terms: 12 + 18n = 18 + 7 + 45n Combine like terms: 18 + 7 = 25 12 + 18n = 25 + 45n Solving 12 + 18n = 25 + 45n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-45n' to each side of the equation. 12 + 18n + -45n = 25 + 45n + -45n Combine like terms: 18n + -45n = -27n 12 + -27n = 25 + 45n + -45n Combine like terms: 45n + -45n = 0 12 + -27n = 25 + 0 12 + -27n = 25 Add '-12' to each side of the equation. 12 + -12 + -27n = 25 + -12 Combine like terms: 12 + -12 = 0 0 + -27n = 25 + -12 -27n = 25 + -12 Combine like terms: 25 + -12 = 13 -27n = 13 Divide each side by '-27'. n = -0.4814814815 Simplifying n = -0.4814814815
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