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Simplifying 2(3c + -2d) + -4(c + -3d) = 0 (3c * 2 + -2d * 2) + -4(c + -3d) = 0 (6c + -4d) + -4(c + -3d) = 0 6c + -4d + (c * -4 + -3d * -4) = 0 6c + -4d + (-4c + 12d) = 0 Reorder the terms: 6c + -4c + -4d + 12d = 0 Combine like terms: 6c + -4c = 2c 2c + -4d + 12d = 0 Combine like terms: -4d + 12d = 8d 2c + 8d = 0 Solving 2c + 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. 2c + 8d + -8d = 0 + -8d Combine like terms: 8d + -8d = 0 2c + 0 = 0 + -8d 2c = 0 + -8d Remove the zero: 2c = -8d Divide each side by '2'. c = -4d Simplifying c = -4d
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