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Simplifying 6(c + -2d) + -1(3c + d) = 0 (c * 6 + -2d * 6) + -1(3c + d) = 0 (6c + -12d) + -1(3c + d) = 0 6c + -12d + (3c * -1 + d * -1) = 0 6c + -12d + (-3c + -1d) = 0 Reorder the terms: 6c + -3c + -12d + -1d = 0 Combine like terms: 6c + -3c = 3c 3c + -12d + -1d = 0 Combine like terms: -12d + -1d = -13d 3c + -13d = 0 Solving 3c + -13d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '13d' to each side of the equation. 3c + -13d + 13d = 0 + 13d Combine like terms: -13d + 13d = 0 3c + 0 = 0 + 13d 3c = 0 + 13d Remove the zero: 3c = 13d Divide each side by '3'. c = 4.333333333d Simplifying c = 4.333333333d
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