C=3(2-C)+7C(C+2)

Solution for C=3(2-C)+7C(C+2) equation:

Simplifying
C = 3(2 + -1C) + 7C(C + 2)
C = (2 * 3 + -1C * 3) + 7C(C + 2)
C = (6 + -3C) + 7C(C + 2)

Reorder the terms:
C = 6 + -3C + 7C(2 + C)
C = 6 + -3C + (2 * 7C + C * 7C)
C = 6 + -3C + (14C + 7C2)

Combine like terms: -3C + 14C = 11C
C = 6 + 11C + 7C2

Solving
C = 6 + 11C + 7C2

Solving for variable 'C'.

Reorder the terms:
-6 + C + -11C + -7C2 = 6 + 11C + 7C2 + -6 + -11C + -7C2

Combine like terms: C + -11C = -10C
-6 + -10C + -7C2 = 6 + 11C + 7C2 + -6 + -11C + -7C2

Reorder the terms:
-6 + -10C + -7C2 = 6 + -6 + 11C + -11C + 7C2 + -7C2

Combine like terms: 6 + -6 = 0
-6 + -10C + -7C2 = 0 + 11C + -11C + 7C2 + -7C2
-6 + -10C + -7C2 = 11C + -11C + 7C2 + -7C2

Combine like terms: 11C + -11C = 0
-6 + -10C + -7C2 = 0 + 7C2 + -7C2
-6 + -10C + -7C2 = 7C2 + -7C2

Combine like terms: 7C2 + -7C2 = 0
-6 + -10C + -7C2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 10C + 7C2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 10C + 7C2)' equal to zero and attempt to solve:

Simplifying
6 + 10C + 7C2 = 0

Solving
6 + 10C + 7C2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
0.8571428571 + 1.428571429C + C2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + 1.428571429C + -0.8571428571 + C2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + 1.428571429C + C2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + 1.428571429C + C2 = 0 + -0.8571428571
1.428571429C + C2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
1.428571429C + C2 = -0.8571428571

The C term is 1.428571429C.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429C + 0.5102040819 + C2 = -0.8571428571 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429C + C2 = -0.8571428571 + 0.5102040819

Combine like terms: -0.8571428571 + 0.5102040819 = -0.3469387752
0.5102040819 + 1.428571429C + C2 = -0.3469387752

Factor a perfect square on the left side:
(C + 0.7142857145)(C + 0.7142857145) = -0.3469387752

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.