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Simplifying 4(c + 5d) + 2(c + -8d) = 0 (c * 4 + 5d * 4) + 2(c + -8d) = 0 (4c + 20d) + 2(c + -8d) = 0 4c + 20d + (c * 2 + -8d * 2) = 0 4c + 20d + (2c + -16d) = 0 Reorder the terms: 4c + 2c + 20d + -16d = 0 Combine like terms: 4c + 2c = 6c 6c + 20d + -16d = 0 Combine like terms: 20d + -16d = 4d 6c + 4d = 0 Solving 6c + 4d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4d' to each side of the equation. 6c + 4d + -4d = 0 + -4d Combine like terms: 4d + -4d = 0 6c + 0 = 0 + -4d 6c = 0 + -4d Remove the zero: 6c = -4d Divide each side by '6'. c = -0.6666666667d Simplifying c = -0.6666666667d
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