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Simplifying 3(5c + 4d) + 6(d + -2c) = 0 (5c * 3 + 4d * 3) + 6(d + -2c) = 0 (15c + 12d) + 6(d + -2c) = 0 Reorder the terms: 15c + 12d + 6(-2c + d) = 0 15c + 12d + (-2c * 6 + d * 6) = 0 15c + 12d + (-12c + 6d) = 0 Reorder the terms: 15c + -12c + 12d + 6d = 0 Combine like terms: 15c + -12c = 3c 3c + 12d + 6d = 0 Combine like terms: 12d + 6d = 18d 3c + 18d = 0 Solving 3c + 18d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-18d' to each side of the equation. 3c + 18d + -18d = 0 + -18d Combine like terms: 18d + -18d = 0 3c + 0 = 0 + -18d 3c = 0 + -18d Remove the zero: 3c = -18d Divide each side by '3'. c = -6d Simplifying c = -6d
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