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Simplifying 3(4c + -1d) + -2(c + 3d) = 0 (4c * 3 + -1d * 3) + -2(c + 3d) = 0 (12c + -3d) + -2(c + 3d) = 0 12c + -3d + (c * -2 + 3d * -2) = 0 12c + -3d + (-2c + -6d) = 0 Reorder the terms: 12c + -2c + -3d + -6d = 0 Combine like terms: 12c + -2c = 10c 10c + -3d + -6d = 0 Combine like terms: -3d + -6d = -9d 10c + -9d = 0 Solving 10c + -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. 10c + -9d + 9d = 0 + 9d Combine like terms: -9d + 9d = 0 10c + 0 = 0 + 9d 10c = 0 + 9d Remove the zero: 10c = 9d Divide each side by '10'. c = 0.9d Simplifying c = 0.9d
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