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Simplifying 12(c + 3d + 4e) + 2(2c + d + 6e) = 0 (c * 12 + 3d * 12 + 4e * 12) + 2(2c + d + 6e) = 0 (12c + 36d + 48e) + 2(2c + d + 6e) = 0 12c + 36d + 48e + (2c * 2 + d * 2 + 6e * 2) = 0 12c + 36d + 48e + (4c + 2d + 12e) = 0 Reorder the terms: 12c + 4c + 36d + 2d + 48e + 12e = 0 Combine like terms: 12c + 4c = 16c 16c + 36d + 2d + 48e + 12e = 0 Combine like terms: 36d + 2d = 38d 16c + 38d + 48e + 12e = 0 Combine like terms: 48e + 12e = 60e 16c + 38d + 60e = 0 Solving 16c + 38d + 60e = 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 + 60e = 0 + -38d Combine like terms: 38d + -38d = 0 16c + 0 + 60e = 0 + -38d 16c + 60e = 0 + -38d Remove the zero: 16c + 60e = -38d Add '-60e' to each side of the equation. 16c + 60e + -60e = -38d + -60e Combine like terms: 60e + -60e = 0 16c + 0 = -38d + -60e 16c = -38d + -60e Divide each side by '16'. c = -2.375d + -3.75e Simplifying c = -2.375d + -3.75e
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