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Simplifying 5(c + -3d) + -1(3c + d) = 0 (c * 5 + -3d * 5) + -1(3c + d) = 0 (5c + -15d) + -1(3c + d) = 0 5c + -15d + (3c * -1 + d * -1) = 0 5c + -15d + (-3c + -1d) = 0 Reorder the terms: 5c + -3c + -15d + -1d = 0 Combine like terms: 5c + -3c = 2c 2c + -15d + -1d = 0 Combine like terms: -15d + -1d = -16d 2c + -16d = 0 Solving 2c + -16d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '16d' to each side of the equation. 2c + -16d + 16d = 0 + 16d Combine like terms: -16d + 16d = 0 2c + 0 = 0 + 16d 2c = 0 + 16d Remove the zero: 2c = 16d Divide each side by '2'. c = 8d Simplifying c = 8d
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