4n^2-8n+2=0

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

Simplifying
4n2 + -8n + 2 = 0

Reorder the terms:
2 + -8n + 4n2 = 0

Solving
2 + -8n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -4n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -4n + 2n2)' equal to zero and attempt to solve:

Simplifying
1 + -4n + 2n2 = 0

Solving
1 + -4n + 2n2 = 0

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

Divide each side by '2'.
0.5 + -2n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2n + n2 = 0 + -0.5
-2n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-2n + n2 = -0.5

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

Add '1' to each side of the equation.
-2n + 1 + n2 = -0.5 + 1

Reorder the terms:
1 + -2n + n2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + -2n + n2 = 0.5

Factor a perfect square on the left side:
(n + -1)(n + -1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(n + -1) equal to 0.707106781 and -0.707106781.

Subproblem 1
n + -1 = 0.707106781

Simplifying
n + -1 = 0.707106781

Reorder the terms:
-1 + n = 0.707106781

Solving
-1 + n = 0.707106781

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = 0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + n = 0.707106781 + 1
n = 0.707106781 + 1

Combine like terms: 0.707106781 + 1 = 1.707106781
n = 1.707106781

Simplifying
n = 1.707106781

Subproblem 2
n + -1 = -0.707106781

Simplifying
n + -1 = -0.707106781

Reorder the terms:
-1 + n = -0.707106781

Solving
-1 + n = -0.707106781

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = -0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + n = -0.707106781 + 1
n = -0.707106781 + 1

Combine like terms: -0.707106781 + 1 = 0.292893219
n = 0.292893219

Simplifying
n = 0.292893219

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.707106781, 0.292893219}
Solution
n = {1.707106781, 0.292893219}