3c^2+2cd^2-c^2=3cd^2-c^2

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Solution for 3c^2+2cd^2-c^2=3cd^2-c^2 equation:


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) = 0

Subproblem 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 = 0

Subproblem 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 = 0.3333333333d2

Solution

c = {0, 0.3333333333d2}

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