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Simplifying 8(c + -2d) + -1(3c + d) = 0 (c * 8 + -2d * 8) + -1(3c + d) = 0 (8c + -16d) + -1(3c + d) = 0 8c + -16d + (3c * -1 + d * -1) = 0 8c + -16d + (-3c + -1d) = 0 Reorder the terms: 8c + -3c + -16d + -1d = 0 Combine like terms: 8c + -3c = 5c 5c + -16d + -1d = 0 Combine like terms: -16d + -1d = -17d 5c + -17d = 0 Solving 5c + -17d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '17d' to each side of the equation. 5c + -17d + 17d = 0 + 17d Combine like terms: -17d + 17d = 0 5c + 0 = 0 + 17d 5c = 0 + 17d Remove the zero: 5c = 17d Divide each side by '5'. c = 3.4d Simplifying c = 3.4d
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