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Simplifying 6(c + -5d) + -1(4c + d) = 0 (c * 6 + -5d * 6) + -1(4c + d) = 0 (6c + -30d) + -1(4c + d) = 0 6c + -30d + (4c * -1 + d * -1) = 0 6c + -30d + (-4c + -1d) = 0 Reorder the terms: 6c + -4c + -30d + -1d = 0 Combine like terms: 6c + -4c = 2c 2c + -30d + -1d = 0 Combine like terms: -30d + -1d = -31d 2c + -31d = 0 Solving 2c + -31d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '31d' to each side of the equation. 2c + -31d + 31d = 0 + 31d Combine like terms: -31d + 31d = 0 2c + 0 = 0 + 31d 2c = 0 + 31d Remove the zero: 2c = 31d Divide each side by '2'. c = 15.5d Simplifying c = 15.5d
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