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Simplifying 5(c + 12) = 3(c + 10) Reorder the terms: 5(12 + c) = 3(c + 10) (12 * 5 + c * 5) = 3(c + 10) (60 + 5c) = 3(c + 10) Reorder the terms: 60 + 5c = 3(10 + c) 60 + 5c = (10 * 3 + c * 3) 60 + 5c = (30 + 3c) Solving 60 + 5c = 30 + 3c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3c' to each side of the equation. 60 + 5c + -3c = 30 + 3c + -3c Combine like terms: 5c + -3c = 2c 60 + 2c = 30 + 3c + -3c Combine like terms: 3c + -3c = 0 60 + 2c = 30 + 0 60 + 2c = 30 Add '-60' to each side of the equation. 60 + -60 + 2c = 30 + -60 Combine like terms: 60 + -60 = 0 0 + 2c = 30 + -60 2c = 30 + -60 Combine like terms: 30 + -60 = -30 2c = -30 Divide each side by '2'. c = -15 Simplifying c = -15
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