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Simplifying 12(c + 3d + 4f) + 2(2c + d + 6f) = 0 (c * 12 + 3d * 12 + 4f * 12) + 2(2c + d + 6f) = 0 (12c + 36d + 48f) + 2(2c + d + 6f) = 0 12c + 36d + 48f + (2c * 2 + d * 2 + 6f * 2) = 0 12c + 36d + 48f + (4c + 2d + 12f) = 0 Reorder the terms: 12c + 4c + 36d + 2d + 48f + 12f = 0 Combine like terms: 12c + 4c = 16c 16c + 36d + 2d + 48f + 12f = 0 Combine like terms: 36d + 2d = 38d 16c + 38d + 48f + 12f = 0 Combine like terms: 48f + 12f = 60f 16c + 38d + 60f = 0 Solving 16c + 38d + 60f = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-38d' to each side of the equation. 16c + 38d + -38d + 60f = 0 + -38d Combine like terms: 38d + -38d = 0 16c + 0 + 60f = 0 + -38d 16c + 60f = 0 + -38d Remove the zero: 16c + 60f = -38d Add '-60f' to each side of the equation. 16c + 60f + -60f = -38d + -60f Combine like terms: 60f + -60f = 0 16c + 0 = -38d + -60f 16c = -38d + -60f Divide each side by '16'. c = -2.375d + -3.75f Simplifying c = -2.375d + -3.75f
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