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Simplifying 7(1 + 5n) + 6(6a + 5) = 32 (1 * 7 + 5n * 7) + 6(6a + 5) = 32 (7 + 35n) + 6(6a + 5) = 32 Reorder the terms: 7 + 35n + 6(5 + 6a) = 32 7 + 35n + (5 * 6 + 6a * 6) = 32 7 + 35n + (30 + 36a) = 32 Reorder the terms: 7 + 30 + 36a + 35n = 32 Combine like terms: 7 + 30 = 37 37 + 36a + 35n = 32 Solving 37 + 36a + 35n = 32 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + 36a + -37 + 35n = 32 + -37 Reorder the terms: 37 + -37 + 36a + 35n = 32 + -37 Combine like terms: 37 + -37 = 0 0 + 36a + 35n = 32 + -37 36a + 35n = 32 + -37 Combine like terms: 32 + -37 = -5 36a + 35n = -5 Add '-35n' to each side of the equation. 36a + 35n + -35n = -5 + -35n Combine like terms: 35n + -35n = 0 36a + 0 = -5 + -35n 36a = -5 + -35n Divide each side by '36'. a = -0.1388888889 + -0.9722222222n Simplifying a = -0.1388888889 + -0.9722222222n
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