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Simplifying 7(c + -4d) + -1(5c + d) = 0 (c * 7 + -4d * 7) + -1(5c + d) = 0 (7c + -28d) + -1(5c + d) = 0 7c + -28d + (5c * -1 + d * -1) = 0 7c + -28d + (-5c + -1d) = 0 Reorder the terms: 7c + -5c + -28d + -1d = 0 Combine like terms: 7c + -5c = 2c 2c + -28d + -1d = 0 Combine like terms: -28d + -1d = -29d 2c + -29d = 0 Solving 2c + -29d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '29d' to each side of the equation. 2c + -29d + 29d = 0 + 29d Combine like terms: -29d + 29d = 0 2c + 0 = 0 + 29d 2c = 0 + 29d Remove the zero: 2c = 29d Divide each side by '2'. c = 14.5d Simplifying c = 14.5d
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