2n*2n-2n=180

Solution for 2n*2n-2n=180 equation:

Simplifying
2n * 2n + -2n = 180

Reorder the terms for easier multiplication:
2 * 2n * n + -2n = 180

Multiply 2 * 2
4n * n + -2n = 180

Multiply n * n
4n2 + -2n = 180

Reorder the terms:
-2n + 4n2 = 180

Solving
-2n + 4n2 = 180

Solving for variable 'n'.

Reorder the terms:
-180 + -2n + 4n2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -2n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -1n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-90 + -1n + 2n2)' equal to zero and attempt to solve:

Simplifying
-90 + -1n + 2n2 = 0

Solving
-90 + -1n + 2n2 = 0

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

Divide each side by '2'.
-45 + -0.5n + n2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -0.5n + 45 + n2 = 0 + 45

Reorder the terms:
-45 + 45 + -0.5n + n2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -0.5n + n2 = 0 + 45
-0.5n + n2 = 0 + 45

Combine like terms: 0 + 45 = 45
-0.5n + n2 = 45

The n term is -0.5n.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5n + 0.0625 + n2 = 45 + 0.0625

Reorder the terms:
0.0625 + -0.5n + n2 = 45 + 0.0625

Combine like terms: 45 + 0.0625 = 45.0625
0.0625 + -0.5n + n2 = 45.0625

Factor a perfect square on the left side:
(n + -0.25)(n + -0.25) = 45.0625

Calculate the square root of the right side: 6.712860791

Break this problem into two subproblems by setting 
(n + -0.25) equal to 6.712860791 and -6.712860791.

Subproblem 1
n + -0.25 = 6.712860791

Simplifying
n + -0.25 = 6.712860791

Reorder the terms:
-0.25 + n = 6.712860791

Solving
-0.25 + n = 6.712860791

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = 6.712860791 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = 6.712860791 + 0.25
n = 6.712860791 + 0.25

Combine like terms: 6.712860791 + 0.25 = 6.962860791
n = 6.962860791

Simplifying
n = 6.962860791

Subproblem 2
n + -0.25 = -6.712860791

Simplifying
n + -0.25 = -6.712860791

Reorder the terms:
-0.25 + n = -6.712860791

Solving
-0.25 + n = -6.712860791

Solving for variable 'n'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + n = -6.712860791 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + n = -6.712860791 + 0.25
n = -6.712860791 + 0.25

Combine like terms: -6.712860791 + 0.25 = -6.462860791
n = -6.462860791

Simplifying
n = -6.462860791

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.962860791, -6.462860791}
Solution
n = {6.962860791, -6.462860791}