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Simplifying 2[5c + -4(3c + -5)] = (4 + 7c) * 3 + -4(8c + -1) Reorder the terms: 2[5c + -4(-5 + 3c)] = (4 + 7c) * 3 + -4(8c + -1) 2[5c + (-5 * -4 + 3c * -4)] = (4 + 7c) * 3 + -4(8c + -1) 2[5c + (20 + -12c)] = (4 + 7c) * 3 + -4(8c + -1) Reorder the terms: 2[20 + 5c + -12c] = (4 + 7c) * 3 + -4(8c + -1) Combine like terms: 5c + -12c = -7c 2[20 + -7c] = (4 + 7c) * 3 + -4(8c + -1) [20 * 2 + -7c * 2] = (4 + 7c) * 3 + -4(8c + -1) [40 + -14c] = (4 + 7c) * 3 + -4(8c + -1) Reorder the terms for easier multiplication: 40 + -14c = 3(4 + 7c) + -4(8c + -1) 40 + -14c = (4 * 3 + 7c * 3) + -4(8c + -1) 40 + -14c = (12 + 21c) + -4(8c + -1) Reorder the terms: 40 + -14c = 12 + 21c + -4(-1 + 8c) 40 + -14c = 12 + 21c + (-1 * -4 + 8c * -4) 40 + -14c = 12 + 21c + (4 + -32c) Reorder the terms: 40 + -14c = 12 + 4 + 21c + -32c Combine like terms: 12 + 4 = 16 40 + -14c = 16 + 21c + -32c Combine like terms: 21c + -32c = -11c 40 + -14c = 16 + -11c Solving 40 + -14c = 16 + -11c Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '11c' to each side of the equation. 40 + -14c + 11c = 16 + -11c + 11c Combine like terms: -14c + 11c = -3c 40 + -3c = 16 + -11c + 11c Combine like terms: -11c + 11c = 0 40 + -3c = 16 + 0 40 + -3c = 16 Add '-40' to each side of the equation. 40 + -40 + -3c = 16 + -40 Combine like terms: 40 + -40 = 0 0 + -3c = 16 + -40 -3c = 16 + -40 Combine like terms: 16 + -40 = -24 -3c = -24 Divide each side by '-3'. c = 8 Simplifying c = 8
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