6(c-1)c=4

Solution for 6(c-1)c=4 equation:

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

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

Reorder the terms for easier multiplication:
6c(-1 + c) = 4
(-1 * 6c + c * 6c) = 4
(-6c + 6c2) = 4

Solving
-6c + 6c2 = 4

Solving for variable 'c'.

Reorder the terms:
-4 + -6c + 6c2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -6c + 6c2 = 0

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

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

Simplifying
-2 + -3c + 3c2 = 0

Solving
-2 + -3c + 3c2 = 0

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

Divide each side by '3'.
-0.6666666667 + -1c + c2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1c + 0.6666666667 + c2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1c + c2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1c + c2 = 0 + 0.6666666667
-1c + c2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1c + c2 = 0.6666666667

The c term is -1c.  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.
-1c + 0.25 + c2 = 0.6666666667 + 0.25

Reorder the terms:
0.25 + -1c + c2 = 0.6666666667 + 0.25

Combine like terms: 0.6666666667 + 0.25 = 0.9166666667
0.25 + -1c + c2 = 0.9166666667

Factor a perfect square on the left side:
(c + -0.5)(c + -0.5) = 0.9166666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(c + -0.5) equal to 0.957427108 and -0.957427108.

Subproblem 1
c + -0.5 = 0.957427108

Simplifying
c + -0.5 = 0.957427108

Reorder the terms:
-0.5 + c = 0.957427108

Solving
-0.5 + c = 0.957427108

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 = 0.957427108 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + c = 0.957427108 + 0.5
c = 0.957427108 + 0.5

Combine like terms: 0.957427108 + 0.5 = 1.457427108
c = 1.457427108

Simplifying
c = 1.457427108

Subproblem 2
c + -0.5 = -0.957427108

Simplifying
c + -0.5 = -0.957427108

Reorder the terms:
-0.5 + c = -0.957427108

Solving
-0.5 + c = -0.957427108

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 = -0.957427108 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + c = -0.957427108 + 0.5
c = -0.957427108 + 0.5

Combine like terms: -0.957427108 + 0.5 = -0.457427108
c = -0.457427108

Simplifying
c = -0.457427108

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.457427108, -0.457427108}
Solution
c = {1.457427108, -0.457427108}