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Simplifying 3c2 + 2cd2 + -1c2 = 3cd2 + -1c2 Reorder the terms: 2cd2 + 3c2 + -1c2 = 3cd2 + -1c2 Combine like terms: 3c2 + -1c2 = 2c2 2cd2 + 2c2 = 3cd2 + -1c2 Solving 2cd2 + 2c2 = 3cd2 + -1c2 Solving for variable 'c'. Reorder the terms: 2cd2 + -3cd2 + 2c2 + c2 = 3cd2 + -1c2 + -3cd2 + c2 Combine like terms: 2cd2 + -3cd2 = -1cd2 -1cd2 + 2c2 + c2 = 3cd2 + -1c2 + -3cd2 + c2 Combine like terms: 2c2 + c2 = 3c2 -1cd2 + 3c2 = 3cd2 + -1c2 + -3cd2 + c2 Reorder the terms: -1cd2 + 3c2 = 3cd2 + -3cd2 + -1c2 + c2 Combine like terms: 3cd2 + -3cd2 = 0 -1cd2 + 3c2 = 0 + -1c2 + c2 -1cd2 + 3c2 = -1c2 + c2 Combine like terms: -1c2 + c2 = 0 -1cd2 + 3c2 = 0 Factor out the Greatest Common Factor (GCF), 'c'. c(-1d2 + 3c) = 0Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(-1d2 + 3c)' equal to zero and attempt to solve: Simplifying -1d2 + 3c = 0 Reorder the terms: 3c + -1d2 = 0 Solving 3c + -1d2 = 0 Move all terms containing c to the left, all other terms to the right. Add 'd2' to each side of the equation. 3c + -1d2 + d2 = 0 + d2 Combine like terms: -1d2 + d2 = 0 3c + 0 = 0 + d2 3c = 0 + d2 Remove the zero: 3c = d2 Divide each side by '3'. c = 0.3333333333d2 Simplifying c = 0.3333333333d2Solution
c = {0, 0.3333333333d2}
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