180(n-2)n=5

Solution for 180(n-2)n=5 equation:

Simplifying
180(n + -2) * n = 5

Reorder the terms:
180(-2 + n) * n = 5

Reorder the terms for easier multiplication:
180n(-2 + n) = 5
(-2 * 180n + n * 180n) = 5
(-360n + 180n2) = 5

Solving
-360n + 180n2 = 5

Solving for variable 'n'.

Reorder the terms:
-5 + -360n + 180n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -360n + 180n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + -72n + 36n2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + -72n + 36n2)' equal to zero and attempt to solve:

Simplifying
-1 + -72n + 36n2 = 0

Solving
-1 + -72n + 36n2 = 0

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

Divide each side by '36'.
-0.02777777778 + -2n + n2 = 0

Move the constant term to the right:

Add '0.02777777778' to each side of the equation.
-0.02777777778 + -2n + 0.02777777778 + n2 = 0 + 0.02777777778

Reorder the terms:
-0.02777777778 + 0.02777777778 + -2n + n2 = 0 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + -2n + n2 = 0 + 0.02777777778
-2n + n2 = 0 + 0.02777777778

Combine like terms: 0 + 0.02777777778 = 0.02777777778
-2n + n2 = 0.02777777778

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 = 0.02777777778 + 1

Reorder the terms:
1 + -2n + n2 = 0.02777777778 + 1

Combine like terms: 0.02777777778 + 1 = 1.02777777778
1 + -2n + n2 = 1.02777777778

Factor a perfect square on the left side:
(n + -1)(n + -1) = 1.02777777778

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(n + -1) equal to 1.013793755 and -1.013793755.

Subproblem 1
n + -1 = 1.013793755

Simplifying
n + -1 = 1.013793755

Reorder the terms:
-1 + n = 1.013793755

Solving
-1 + n = 1.013793755

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 = 1.013793755 + 1

Combine like terms: -1 + 1 = 0
0 + n = 1.013793755 + 1
n = 1.013793755 + 1

Combine like terms: 1.013793755 + 1 = 2.013793755
n = 2.013793755

Simplifying
n = 2.013793755

Subproblem 2
n + -1 = -1.013793755

Simplifying
n + -1 = -1.013793755

Reorder the terms:
-1 + n = -1.013793755

Solving
-1 + n = -1.013793755

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 = -1.013793755 + 1

Combine like terms: -1 + 1 = 0
0 + n = -1.013793755 + 1
n = -1.013793755 + 1

Combine like terms: -1.013793755 + 1 = -0.013793755
n = -0.013793755

Simplifying
n = -0.013793755

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.013793755, -0.013793755}
Solution
n = {2.013793755, -0.013793755}