4c^2+8c-4=0

Solution for 4c^2+8c-4=0 equation:

Simplifying
4c2 + 8c + -4 = 0

Reorder the terms:
-4 + 8c + 4c2 = 0

Solving
-4 + 8c + 4c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 2c + c2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 2c + c2)' equal to zero and attempt to solve:

Simplifying
-1 + 2c + c2 = 0

Solving
-1 + 2c + c2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + 2c + c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2c + c2 = 0 + 1
2c + c2 = 0 + 1

Combine like terms: 0 + 1 = 1
2c + c2 = 1

The c term is 2c.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2c + 1 + c2 = 1 + 1

Reorder the terms:
1 + 2c + c2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + 2c + c2 = 2

Factor a perfect square on the left side:
(c + 1)(c + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(c + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
c + 1 = 1.414213562

Simplifying
c + 1 = 1.414213562

Reorder the terms:
1 + c = 1.414213562

Solving
1 + c = 1.414213562

Solving for variable 'c'.

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

Add '-1' to each side of the equation.
1 + -1 + c = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + c = 1.414213562 + -1
c = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
c = 0.414213562

Simplifying
c = 0.414213562

Subproblem 2
c + 1 = -1.414213562

Simplifying
c + 1 = -1.414213562

Reorder the terms:
1 + c = -1.414213562

Solving
1 + c = -1.414213562

Solving for variable 'c'.

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

Add '-1' to each side of the equation.
1 + -1 + c = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + c = -1.414213562 + -1
c = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
c = -2.414213562

Simplifying
c = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.414213562, -2.414213562}
Solution
c = {0.414213562, -2.414213562}