12c^2-12d^2=c^2-2cd+d^2

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Solution for 12c^2-12d^2=c^2-2cd+d^2 equation: 


Simplifying
12c2 + -12d2 = c2 + -2cd + d2

Reorder the terms:
12c2 + -12d2 = -2cd + c2 + d2

Solving
12c2 + -12d2 = -2cd + c2 + d2

Solving for variable 'c'.

Reorder the terms:
2cd + 12c2 + -1c2 + -12d2 + -1d2 = -2cd + c2 + d2 + 2cd + -1c2 + -1d2

Combine like terms: 12c2 + -1c2 = 11c2
2cd + 11c2 + -12d2 + -1d2 = -2cd + c2 + d2 + 2cd + -1c2 + -1d2

Combine like terms: -12d2 + -1d2 = -13d2
2cd + 11c2 + -13d2 = -2cd + c2 + d2 + 2cd + -1c2 + -1d2

Reorder the terms:
2cd + 11c2 + -13d2 = -2cd + 2cd + c2 + -1c2 + d2 + -1d2

Combine like terms: -2cd + 2cd = 0
2cd + 11c2 + -13d2 = 0 + c2 + -1c2 + d2 + -1d2
2cd + 11c2 + -13d2 = c2 + -1c2 + d2 + -1d2

Combine like terms: c2 + -1c2 = 0
2cd + 11c2 + -13d2 = 0 + d2 + -1d2
2cd + 11c2 + -13d2 = d2 + -1d2

Combine like terms: d2 + -1d2 = 0
2cd + 11c2 + -13d2 = 0

Factor a trinomial.
(c + -1d)(11c + 13d) = 0


Subproblem 1
Set the factor '(c + -1d)' equal to zero and attempt to solve:

Simplifying
c + -1d = 0

Solving
c + -1d = 0

Move all terms containing c to the left, all other terms to the right.

Add 'd' to each side of the equation.
c + -1d + d = 0 + d

Combine like terms: -1d + d = 0
c + 0 = 0 + d
c = 0 + d
Remove the zero:
c = d

Simplifying
c = d

Subproblem 2
Set the factor '(11c + 13d)' equal to zero and attempt to solve:

Simplifying
11c + 13d = 0

Solving
11c + 13d = 0

Move all terms containing c to the left, all other terms to the right.

Add '-13d' to each side of the equation.
11c + 13d + -13d = 0 + -13d

Combine like terms: 13d + -13d = 0
11c + 0 = 0 + -13d
11c = 0 + -13d
Remove the zero:
11c = -13d

Divide each side by '11'.
c = -1.181818182d

Simplifying
c = -1.181818182d
Solution
c = {d, -1.181818182d}

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