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Simplifying 0.5(10 + 12n) = 0.3(15n + 15) (10 * 0.5 + 12n * 0.5) = 0.3(15n + 15) (5 + 6n) = 0.3(15n + 15) Reorder the terms: 5 + 6n = 0.3(15 + 15n) 5 + 6n = (15 * 0.3 + 15n * 0.3) 5 + 6n = (4.5 + 4.5n) Solving 5 + 6n = 4.5 + 4.5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.5n' to each side of the equation. 5 + 6n + -4.5n = 4.5 + 4.5n + -4.5n Combine like terms: 6n + -4.5n = 1.5n 5 + 1.5n = 4.5 + 4.5n + -4.5n Combine like terms: 4.5n + -4.5n = 0.0 5 + 1.5n = 4.5 + 0.0 5 + 1.5n = 4.5 Add '-5' to each side of the equation. 5 + -5 + 1.5n = 4.5 + -5 Combine like terms: 5 + -5 = 0 0 + 1.5n = 4.5 + -5 1.5n = 4.5 + -5 Combine like terms: 4.5 + -5 = -0.5 1.5n = -0.5 Divide each side by '1.5'. n = -0.3333333333 Simplifying n = -0.3333333333
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