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Simplifying 6(5n + -3) + 7(6n + -4) = -5(6n + -1) Reorder the terms: 6(-3 + 5n) + 7(6n + -4) = -5(6n + -1) (-3 * 6 + 5n * 6) + 7(6n + -4) = -5(6n + -1) (-18 + 30n) + 7(6n + -4) = -5(6n + -1) Reorder the terms: -18 + 30n + 7(-4 + 6n) = -5(6n + -1) -18 + 30n + (-4 * 7 + 6n * 7) = -5(6n + -1) -18 + 30n + (-28 + 42n) = -5(6n + -1) Reorder the terms: -18 + -28 + 30n + 42n = -5(6n + -1) Combine like terms: -18 + -28 = -46 -46 + 30n + 42n = -5(6n + -1) Combine like terms: 30n + 42n = 72n -46 + 72n = -5(6n + -1) Reorder the terms: -46 + 72n = -5(-1 + 6n) -46 + 72n = (-1 * -5 + 6n * -5) -46 + 72n = (5 + -30n) Solving -46 + 72n = 5 + -30n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '30n' to each side of the equation. -46 + 72n + 30n = 5 + -30n + 30n Combine like terms: 72n + 30n = 102n -46 + 102n = 5 + -30n + 30n Combine like terms: -30n + 30n = 0 -46 + 102n = 5 + 0 -46 + 102n = 5 Add '46' to each side of the equation. -46 + 46 + 102n = 5 + 46 Combine like terms: -46 + 46 = 0 0 + 102n = 5 + 46 102n = 5 + 46 Combine like terms: 5 + 46 = 51 102n = 51 Divide each side by '102'. n = 0.5 Simplifying n = 0.5
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