6(c+1)c=6

Solution for 6(c+1)c=6 equation:

Simplifying
6(c + 1) * c = 6

Reorder the terms:
6(1 + c) * c = 6

Reorder the terms for easier multiplication:
6c(1 + c) = 6
(1 * 6c + c * 6c) = 6
(6c + 6c2) = 6

Solving
6c + 6c2 = 6

Solving for variable 'c'.

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + c + c2) = 0

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

Simplifying
-1 + c + c2 = 0

Solving
-1 + c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + c + c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + c + c2 = 0 + 1
c + c2 = 0 + 1

Combine like terms: 0 + 1 = 1
c + c2 = 1

The c term is c.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
c + 0.25 + c2 = 1 + 0.25

Reorder the terms:
0.25 + c + c2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + c + c2 = 1.25

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(c + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
c + 0.5 = 1.118033989

Simplifying
c + 0.5 = 1.118033989

Reorder the terms:
0.5 + c = 1.118033989

Solving
0.5 + c = 1.118033989

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 1.118033989 + -0.5
c = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
c = 0.618033989

Simplifying
c = 0.618033989

Subproblem 2
c + 0.5 = -1.118033989

Simplifying
c + 0.5 = -1.118033989

Reorder the terms:
0.5 + c = -1.118033989

Solving
0.5 + c = -1.118033989

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -1.118033989 + -0.5
c = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
c = -1.618033989

Simplifying
c = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.618033989, -1.618033989}
Solution
c = {0.618033989, -1.618033989}