31-(2c+4)=2(c+6)c

Solution for 31-(2c+4)=2(c+6)c equation:

Simplifying
31 + -1(2c + 4) = 2(c + 6) * c

Reorder the terms:
31 + -1(4 + 2c) = 2(c + 6) * c
31 + (4 * -1 + 2c * -1) = 2(c + 6) * c
31 + (-4 + -2c) = 2(c + 6) * c

Combine like terms: 31 + -4 = 27
27 + -2c = 2(c + 6) * c

Reorder the terms:
27 + -2c = 2(6 + c) * c

Reorder the terms for easier multiplication:
27 + -2c = 2c(6 + c)
27 + -2c = (6 * 2c + c * 2c)
27 + -2c = (12c + 2c2)

Solving
27 + -2c = 12c + 2c2

Solving for variable 'c'.

Combine like terms: -2c + -12c = -14c
27 + -14c + -2c2 = 12c + 2c2 + -12c + -2c2

Reorder the terms:
27 + -14c + -2c2 = 12c + -12c + 2c2 + -2c2

Combine like terms: 12c + -12c = 0
27 + -14c + -2c2 = 0 + 2c2 + -2c2
27 + -14c + -2c2 = 2c2 + -2c2

Combine like terms: 2c2 + -2c2 = 0
27 + -14c + -2c2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-13.5 + 7c + c2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + 7c + 13.5 + c2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + 7c + c2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + 7c + c2 = 0 + 13.5
7c + c2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
7c + c2 = 13.5

The c term is 7c.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7c + 12.25 + c2 = 13.5 + 12.25

Reorder the terms:
12.25 + 7c + c2 = 13.5 + 12.25

Combine like terms: 13.5 + 12.25 = 25.75
12.25 + 7c + c2 = 25.75

Factor a perfect square on the left side:
(c + 3.5)(c + 3.5) = 25.75

Calculate the square root of the right side: 5.074445783

Break this problem into two subproblems by setting 
(c + 3.5) equal to 5.074445783 and -5.074445783.

Subproblem 1
c + 3.5 = 5.074445783

Simplifying
c + 3.5 = 5.074445783

Reorder the terms:
3.5 + c = 5.074445783

Solving
3.5 + c = 5.074445783

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = 5.074445783 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = 5.074445783 + -3.5
c = 5.074445783 + -3.5

Combine like terms: 5.074445783 + -3.5 = 1.574445783
c = 1.574445783

Simplifying
c = 1.574445783

Subproblem 2
c + 3.5 = -5.074445783

Simplifying
c + 3.5 = -5.074445783

Reorder the terms:
3.5 + c = -5.074445783

Solving
3.5 + c = -5.074445783

Solving for variable 'c'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + c = -5.074445783 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + c = -5.074445783 + -3.5
c = -5.074445783 + -3.5

Combine like terms: -5.074445783 + -3.5 = -8.574445783
c = -8.574445783

Simplifying
c = -8.574445783

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.574445783, -8.574445783}