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Simplifying 2(3c + 2d) + -2(5c + -3d) = 0 (3c * 2 + 2d * 2) + -2(5c + -3d) = 0 (6c + 4d) + -2(5c + -3d) = 0 6c + 4d + (5c * -2 + -3d * -2) = 0 6c + 4d + (-10c + 6d) = 0 Reorder the terms: 6c + -10c + 4d + 6d = 0 Combine like terms: 6c + -10c = -4c -4c + 4d + 6d = 0 Combine like terms: 4d + 6d = 10d -4c + 10d = 0 Solving -4c + 10d = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10d' to each side of the equation. -4c + 10d + -10d = 0 + -10d Combine like terms: 10d + -10d = 0 -4c + 0 = 0 + -10d -4c = 0 + -10d Remove the zero: -4c = -10d Divide each side by '-4'. c = 2.5d Simplifying c = 2.5d
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