2(c+6)c=6

Solution for 2(c+6)c=6 equation:

Simplifying
2(c + 6) * c = 6

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

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

Solving
12c + 2c2 = 6

Solving for variable 'c'.

Reorder the terms:
-6 + 12c + 2c2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 12c + 2c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 6c + c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 6c + c2)' equal to zero and attempt to solve:

Simplifying
-3 + 6c + c2 = 0

Solving
-3 + 6c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6c + 3 + c2 = 0 + 3

Reorder the terms:
-3 + 3 + 6c + c2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6c + c2 = 0 + 3
6c + c2 = 0 + 3

Combine like terms: 0 + 3 = 3
6c + c2 = 3

The c term is 6c.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6c + 9 + c2 = 3 + 9

Reorder the terms:
9 + 6c + c2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6c + c2 = 12

Factor a perfect square on the left side:
(c + 3)(c + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(c + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1
c + 3 = 3.464101615

Simplifying
c + 3 = 3.464101615

Reorder the terms:
3 + c = 3.464101615

Solving
3 + c = 3.464101615

Solving for variable 'c'.

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

Add '-3' to each side of the equation.
3 + -3 + c = 3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + c = 3.464101615 + -3
c = 3.464101615 + -3

Combine like terms: 3.464101615 + -3 = 0.464101615
c = 0.464101615

Simplifying
c = 0.464101615

Subproblem 2
c + 3 = -3.464101615

Simplifying
c + 3 = -3.464101615

Reorder the terms:
3 + c = -3.464101615

Solving
3 + c = -3.464101615

Solving for variable 'c'.

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

Add '-3' to each side of the equation.
3 + -3 + c = -3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + c = -3.464101615 + -3
c = -3.464101615 + -3

Combine like terms: -3.464101615 + -3 = -6.464101615
c = -6.464101615

Simplifying
c = -6.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.464101615, -6.464101615}
Solution
c = {0.464101615, -6.464101615}