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Simplifying 7(c + -5d) + -1(3c + d) = 0 (c * 7 + -5d * 7) + -1(3c + d) = 0 (7c + -35d) + -1(3c + d) = 0 7c + -35d + (3c * -1 + d * -1) = 0 7c + -35d + (-3c + -1d) = 0 Reorder the terms: 7c + -3c + -35d + -1d = 0 Combine like terms: 7c + -3c = 4c 4c + -35d + -1d = 0 Combine like terms: -35d + -1d = -36d 4c + -36d = 0 Solving 4c + -36d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '36d' to each side of the equation. 4c + -36d + 36d = 0 + 36d Combine like terms: -36d + 36d = 0 4c + 0 = 0 + 36d 4c = 0 + 36d Remove the zero: 4c = 36d Divide each side by '4'. c = 9d Simplifying c = 9d
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