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Simplifying -2(-8c + 10) + -5(c + -1) = 6(c + 6) + -2(c + 1) Reorder the terms: -2(10 + -8c) + -5(c + -1) = 6(c + 6) + -2(c + 1) (10 * -2 + -8c * -2) + -5(c + -1) = 6(c + 6) + -2(c + 1) (-20 + 16c) + -5(c + -1) = 6(c + 6) + -2(c + 1) Reorder the terms: -20 + 16c + -5(-1 + c) = 6(c + 6) + -2(c + 1) -20 + 16c + (-1 * -5 + c * -5) = 6(c + 6) + -2(c + 1) -20 + 16c + (5 + -5c) = 6(c + 6) + -2(c + 1) Reorder the terms: -20 + 5 + 16c + -5c = 6(c + 6) + -2(c + 1) Combine like terms: -20 + 5 = -15 -15 + 16c + -5c = 6(c + 6) + -2(c + 1) Combine like terms: 16c + -5c = 11c -15 + 11c = 6(c + 6) + -2(c + 1) Reorder the terms: -15 + 11c = 6(6 + c) + -2(c + 1) -15 + 11c = (6 * 6 + c * 6) + -2(c + 1) -15 + 11c = (36 + 6c) + -2(c + 1) Reorder the terms: -15 + 11c = 36 + 6c + -2(1 + c) -15 + 11c = 36 + 6c + (1 * -2 + c * -2) -15 + 11c = 36 + 6c + (-2 + -2c) Reorder the terms: -15 + 11c = 36 + -2 + 6c + -2c Combine like terms: 36 + -2 = 34 -15 + 11c = 34 + 6c + -2c Combine like terms: 6c + -2c = 4c -15 + 11c = 34 + 4c Solving -15 + 11c = 34 + 4c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4c' to each side of the equation. -15 + 11c + -4c = 34 + 4c + -4c Combine like terms: 11c + -4c = 7c -15 + 7c = 34 + 4c + -4c Combine like terms: 4c + -4c = 0 -15 + 7c = 34 + 0 -15 + 7c = 34 Add '15' to each side of the equation. -15 + 15 + 7c = 34 + 15 Combine like terms: -15 + 15 = 0 0 + 7c = 34 + 15 7c = 34 + 15 Combine like terms: 34 + 15 = 49 7c = 49 Divide each side by '7'. c = 7 Simplifying c = 7
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