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Simplifying 5(c + -3d) + -12c + d = 0 (c * 5 + -3d * 5) + -12c + d = 0 (5c + -15d) + -12c + d = 0 Reorder the terms: 5c + -12c + -15d + d = 0 Combine like terms: 5c + -12c = -7c -7c + -15d + d = 0 Combine like terms: -15d + d = -14d -7c + -14d = 0 Solving -7c + -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. -7c + -14d + 14d = 0 + 14d Combine like terms: -14d + 14d = 0 -7c + 0 = 0 + 14d -7c = 0 + 14d Remove the zero: -7c = 14d Divide each side by '-7'. c = -2d Simplifying c = -2d
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