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Simplifying 8(c + -2d) + -1(5c + d) = 0 (c * 8 + -2d * 8) + -1(5c + d) = 0 (8c + -16d) + -1(5c + d) = 0 8c + -16d + (5c * -1 + d * -1) = 0 8c + -16d + (-5c + -1d) = 0 Reorder the terms: 8c + -5c + -16d + -1d = 0 Combine like terms: 8c + -5c = 3c 3c + -16d + -1d = 0 Combine like terms: -16d + -1d = -17d 3c + -17d = 0 Solving 3c + -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. 3c + -17d + 17d = 0 + 17d Combine like terms: -17d + 17d = 0 3c + 0 = 0 + 17d 3c = 0 + 17d Remove the zero: 3c = 17d Divide each side by '3'. c = 5.666666667d Simplifying c = 5.666666667d
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