(2n-1)(4n-1)=4n^2

Solution for (2n-1)(4n-1)=4n^2 equation:

Simplifying
(2n + -1)(4n + -1) = 4n2

Reorder the terms:
(-1 + 2n)(4n + -1) = 4n2

Reorder the terms:
(-1 + 2n)(-1 + 4n) = 4n2

Multiply (-1 + 2n) * (-1 + 4n)
(-1(-1 + 4n) + 2n * (-1 + 4n)) = 4n2
((-1 * -1 + 4n * -1) + 2n * (-1 + 4n)) = 4n2
((1 + -4n) + 2n * (-1 + 4n)) = 4n2
(1 + -4n + (-1 * 2n + 4n * 2n)) = 4n2
(1 + -4n + (-2n + 8n2)) = 4n2

Combine like terms: -4n + -2n = -6n
(1 + -6n + 8n2) = 4n2

Solving
1 + -6n + 8n2 = 4n2

Solving for variable 'n'.

Combine like terms: 8n2 + -4n2 = 4n2
1 + -6n + 4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
1 + -6n + 4n2 = 0

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

Divide each side by '4'.
0.25 + -1.5n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.5n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.5n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.5n + n2 = 0 + -0.25
-1.5n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.5n + n2 = -0.25

The n term is -1.5n.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5n + 0.5625 + n2 = -0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5n + n2 = -0.25 + 0.5625

Combine like terms: -0.25 + 0.5625 = 0.3125
0.5625 + -1.5n + n2 = 0.3125

Factor a perfect square on the left side:
(n + -0.75)(n + -0.75) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(n + -0.75) equal to 0.559016994 and -0.559016994.

Subproblem 1
n + -0.75 = 0.559016994

Simplifying
n + -0.75 = 0.559016994

Reorder the terms:
-0.75 + n = 0.559016994

Solving
-0.75 + n = 0.559016994

Solving for variable 'n'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + n = 0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + n = 0.559016994 + 0.75
n = 0.559016994 + 0.75

Combine like terms: 0.559016994 + 0.75 = 1.309016994
n = 1.309016994

Simplifying
n = 1.309016994

Subproblem 2
n + -0.75 = -0.559016994

Simplifying
n + -0.75 = -0.559016994

Reorder the terms:
-0.75 + n = -0.559016994

Solving
-0.75 + n = -0.559016994

Solving for variable 'n'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + n = -0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + n = -0.559016994 + 0.75
n = -0.559016994 + 0.75

Combine like terms: -0.559016994 + 0.75 = 0.190983006
n = 0.190983006

Simplifying
n = 0.190983006

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.309016994, 0.190983006}