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Simplifying 8(c + -3d) + -1(4c + d) = 0 (c * 8 + -3d * 8) + -1(4c + d) = 0 (8c + -24d) + -1(4c + d) = 0 8c + -24d + (4c * -1 + d * -1) = 0 8c + -24d + (-4c + -1d) = 0 Reorder the terms: 8c + -4c + -24d + -1d = 0 Combine like terms: 8c + -4c = 4c 4c + -24d + -1d = 0 Combine like terms: -24d + -1d = -25d 4c + -25d = 0 Solving 4c + -25d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '25d' to each side of the equation. 4c + -25d + 25d = 0 + 25d Combine like terms: -25d + 25d = 0 4c + 0 = 0 + 25d 4c = 0 + 25d Remove the zero: 4c = 25d Divide each side by '4'. c = 6.25d Simplifying c = 6.25d
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