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Simplifying 5(3c + -1d) + -1(8c + d) = 0 (3c * 5 + -1d * 5) + -1(8c + d) = 0 (15c + -5d) + -1(8c + d) = 0 15c + -5d + (8c * -1 + d * -1) = 0 15c + -5d + (-8c + -1d) = 0 Reorder the terms: 15c + -8c + -5d + -1d = 0 Combine like terms: 15c + -8c = 7c 7c + -5d + -1d = 0 Combine like terms: -5d + -1d = -6d 7c + -6d = 0 Solving 7c + -6d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6d' to each side of the equation. 7c + -6d + 6d = 0 + 6d Combine like terms: -6d + 6d = 0 7c + 0 = 0 + 6d 7c = 0 + 6d Remove the zero: 7c = 6d Divide each side by '7'. c = 0.8571428571d Simplifying c = 0.8571428571d
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