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Simplifying 5(3n + 2) = 9(4n + 3) + 6 Reorder the terms: 5(2 + 3n) = 9(4n + 3) + 6 (2 * 5 + 3n * 5) = 9(4n + 3) + 6 (10 + 15n) = 9(4n + 3) + 6 Reorder the terms: 10 + 15n = 9(3 + 4n) + 6 10 + 15n = (3 * 9 + 4n * 9) + 6 10 + 15n = (27 + 36n) + 6 Reorder the terms: 10 + 15n = 27 + 6 + 36n Combine like terms: 27 + 6 = 33 10 + 15n = 33 + 36n Solving 10 + 15n = 33 + 36n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-36n' to each side of the equation. 10 + 15n + -36n = 33 + 36n + -36n Combine like terms: 15n + -36n = -21n 10 + -21n = 33 + 36n + -36n Combine like terms: 36n + -36n = 0 10 + -21n = 33 + 0 10 + -21n = 33 Add '-10' to each side of the equation. 10 + -10 + -21n = 33 + -10 Combine like terms: 10 + -10 = 0 0 + -21n = 33 + -10 -21n = 33 + -10 Combine like terms: 33 + -10 = 23 -21n = 23 Divide each side by '-21'. n = -1.095238095 Simplifying n = -1.095238095
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