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Simplifying 6(3n + 2) = 9(5n + 9) + 2 Reorder the terms: 6(2 + 3n) = 9(5n + 9) + 2 (2 * 6 + 3n * 6) = 9(5n + 9) + 2 (12 + 18n) = 9(5n + 9) + 2 Reorder the terms: 12 + 18n = 9(9 + 5n) + 2 12 + 18n = (9 * 9 + 5n * 9) + 2 12 + 18n = (81 + 45n) + 2 Reorder the terms: 12 + 18n = 81 + 2 + 45n Combine like terms: 81 + 2 = 83 12 + 18n = 83 + 45n Solving 12 + 18n = 83 + 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 = 83 + 45n + -45n Combine like terms: 18n + -45n = -27n 12 + -27n = 83 + 45n + -45n Combine like terms: 45n + -45n = 0 12 + -27n = 83 + 0 12 + -27n = 83 Add '-12' to each side of the equation. 12 + -12 + -27n = 83 + -12 Combine like terms: 12 + -12 = 0 0 + -27n = 83 + -12 -27n = 83 + -12 Combine like terms: 83 + -12 = 71 -27n = 71 Divide each side by '-27'. n = -2.62962963 Simplifying n = -2.62962963
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