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Simplifying 12(2n + 1) = 10(3n + -3) Reorder the terms: 12(1 + 2n) = 10(3n + -3) (1 * 12 + 2n * 12) = 10(3n + -3) (12 + 24n) = 10(3n + -3) Reorder the terms: 12 + 24n = 10(-3 + 3n) 12 + 24n = (-3 * 10 + 3n * 10) 12 + 24n = (-30 + 30n) Solving 12 + 24n = -30 + 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. 12 + 24n + -30n = -30 + 30n + -30n Combine like terms: 24n + -30n = -6n 12 + -6n = -30 + 30n + -30n Combine like terms: 30n + -30n = 0 12 + -6n = -30 + 0 12 + -6n = -30 Add '-12' to each side of the equation. 12 + -12 + -6n = -30 + -12 Combine like terms: 12 + -12 = 0 0 + -6n = -30 + -12 -6n = -30 + -12 Combine like terms: -30 + -12 = -42 -6n = -42 Divide each side by '-6'. n = 7 Simplifying n = 7
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