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Simplifying 5(4c + -2d) + 2d + -6(d + -3c) = 0 (4c * 5 + -2d * 5) + 2d + -6(d + -3c) = 0 (20c + -10d) + 2d + -6(d + -3c) = 0 Reorder the terms: 20c + -10d + 2d + -6(-3c + d) = 0 20c + -10d + 2d + (-3c * -6 + d * -6) = 0 20c + -10d + 2d + (18c + -6d) = 0 Reorder the terms: 20c + 18c + -10d + 2d + -6d = 0 Combine like terms: 20c + 18c = 38c 38c + -10d + 2d + -6d = 0 Combine like terms: -10d + 2d = -8d 38c + -8d + -6d = 0 Combine like terms: -8d + -6d = -14d 38c + -14d = 0 Solving 38c + -14d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '14d' to each side of the equation. 38c + -14d + 14d = 0 + 14d Combine like terms: -14d + 14d = 0 38c + 0 = 0 + 14d 38c = 0 + 14d Remove the zero: 38c = 14d Divide each side by '38'. c = 0.3684210526d Simplifying c = 0.3684210526d
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