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Simplifying 6(2c + -1d) + 2(c + -1d) = 0 (2c * 6 + -1d * 6) + 2(c + -1d) = 0 (12c + -6d) + 2(c + -1d) = 0 12c + -6d + (c * 2 + -1d * 2) = 0 12c + -6d + (2c + -2d) = 0 Reorder the terms: 12c + 2c + -6d + -2d = 0 Combine like terms: 12c + 2c = 14c 14c + -6d + -2d = 0 Combine like terms: -6d + -2d = -8d 14c + -8d = 0 Solving 14c + -8d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '8d' to each side of the equation. 14c + -8d + 8d = 0 + 8d Combine like terms: -8d + 8d = 0 14c + 0 = 0 + 8d 14c = 0 + 8d Remove the zero: 14c = 8d Divide each side by '14'. c = 0.5714285714d Simplifying c = 0.5714285714d
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