4(c-1)c=2

Solution for 4(c-1)c=2 equation:

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

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

Reorder the terms for easier multiplication:
4c(-1 + c) = 2
(-1 * 4c + c * 4c) = 2
(-4c + 4c2) = 2

Solving
-4c + 4c2 = 2

Solving for variable 'c'.

Reorder the terms:
-2 + -4c + 4c2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -4c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2c + 2c2) = 0

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

Simplifying
-1 + -2c + 2c2 = 0

Solving
-1 + -2c + 2c2 = 0

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

Divide each side by '2'.
-0.5 + -1c + c2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1c + 0.5 + c2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1c + c2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1c + c2 = 0 + 0.5
-1c + c2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1c + c2 = 0.5

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 = 0.5 + 0.25

Reorder the terms:
0.25 + -1c + c2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + -1c + c2 = 0.75

Factor a perfect square on the left side:
(c + -0.5)(c + -0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(c + -0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
c + -0.5 = 0.866025404

Simplifying
c + -0.5 = 0.866025404

Reorder the terms:
-0.5 + c = 0.866025404

Solving
-0.5 + c = 0.866025404

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 = 0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + c = 0.866025404 + 0.5
c = 0.866025404 + 0.5

Combine like terms: 0.866025404 + 0.5 = 1.366025404
c = 1.366025404

Simplifying
c = 1.366025404

Subproblem 2
c + -0.5 = -0.866025404

Simplifying
c + -0.5 = -0.866025404

Reorder the terms:
-0.5 + c = -0.866025404

Solving
-0.5 + c = -0.866025404

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 = -0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + c = -0.866025404 + 0.5
c = -0.866025404 + 0.5

Combine like terms: -0.866025404 + 0.5 = -0.366025404
c = -0.366025404

Simplifying
c = -0.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.366025404, -0.366025404}
Solution
c = {1.366025404, -0.366025404}