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Simplifying -30 + 3c + -7(2 + -3c) = 4(c + -5) + 3c + 27 -30 + 3c + (2 * -7 + -3c * -7) = 4(c + -5) + 3c + 27 -30 + 3c + (-14 + 21c) = 4(c + -5) + 3c + 27 Reorder the terms: -30 + -14 + 3c + 21c = 4(c + -5) + 3c + 27 Combine like terms: -30 + -14 = -44 -44 + 3c + 21c = 4(c + -5) + 3c + 27 Combine like terms: 3c + 21c = 24c -44 + 24c = 4(c + -5) + 3c + 27 Reorder the terms: -44 + 24c = 4(-5 + c) + 3c + 27 -44 + 24c = (-5 * 4 + c * 4) + 3c + 27 -44 + 24c = (-20 + 4c) + 3c + 27 Reorder the terms: -44 + 24c = -20 + 27 + 4c + 3c Combine like terms: -20 + 27 = 7 -44 + 24c = 7 + 4c + 3c Combine like terms: 4c + 3c = 7c -44 + 24c = 7 + 7c Solving -44 + 24c = 7 + 7c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7c' to each side of the equation. -44 + 24c + -7c = 7 + 7c + -7c Combine like terms: 24c + -7c = 17c -44 + 17c = 7 + 7c + -7c Combine like terms: 7c + -7c = 0 -44 + 17c = 7 + 0 -44 + 17c = 7 Add '44' to each side of the equation. -44 + 44 + 17c = 7 + 44 Combine like terms: -44 + 44 = 0 0 + 17c = 7 + 44 17c = 7 + 44 Combine like terms: 7 + 44 = 51 17c = 51 Divide each side by '17'. c = 3 Simplifying c = 3
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