12c^2-5cd-2d^2=0

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Solution for 12c^2-5cd-2d^2=0 equation: 


Simplifying
12c2 + -5cd + -2d2 = 0

Reorder the terms:
-5cd + 12c2 + -2d2 = 0

Solving
-5cd + 12c2 + -2d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(3c + -2d)(4c + d) = 0


Subproblem 1
Set the factor '(3c + -2d)' equal to zero and attempt to solve:

Simplifying
3c + -2d = 0

Solving
3c + -2d = 0

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

Add '2d' to each side of the equation.
3c + -2d + 2d = 0 + 2d

Combine like terms: -2d + 2d = 0
3c + 0 = 0 + 2d
3c = 0 + 2d
Remove the zero:
3c = 2d

Divide each side by '3'.
c = 0.6666666667d

Simplifying
c = 0.6666666667d

Subproblem 2
Set the factor '(4c + d)' equal to zero and attempt to solve:

Simplifying
4c + d = 0

Solving
4c + d = 0

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

Add '-1d' to each side of the equation.
4c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
4c + 0 = 0 + -1d
4c = 0 + -1d
Remove the zero:
4c = -1d

Divide each side by '4'.
c = -0.25d

Simplifying
c = -0.25d
Solution
c = {0.6666666667d, -0.25d}

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