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Simplifying 2(3c + -4d) + -1(2c + d) = 0 (3c * 2 + -4d * 2) + -1(2c + d) = 0 (6c + -8d) + -1(2c + d) = 0 6c + -8d + (2c * -1 + d * -1) = 0 6c + -8d + (-2c + -1d) = 0 Reorder the terms: 6c + -2c + -8d + -1d = 0 Combine like terms: 6c + -2c = 4c 4c + -8d + -1d = 0 Combine like terms: -8d + -1d = -9d 4c + -9d = 0 Solving 4c + -9d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '9d' to each side of the equation. 4c + -9d + 9d = 0 + 9d Combine like terms: -9d + 9d = 0 4c + 0 = 0 + 9d 4c = 0 + 9d Remove the zero: 4c = 9d Divide each side by '4'. c = 2.25d Simplifying c = 2.25d
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