165=n(180(n-2))

Solution for 165=n(180(n-2)) equation:

Simplifying
165 = n(180(n + -2))

Reorder the terms:
165 = n(180(-2 + n))
165 = n((-2 * 180 + n * 180))
165 = n((-360 + 180n))
165 = (-360 * n + 180n * n)
165 = (-360n + 180n2)

Solving
165 = -360n + 180n2

Solving for variable 'n'.

Reorder the terms:
165 + 360n + -180n2 = -360n + 360n + 180n2 + -180n2

Combine like terms: -360n + 360n = 0
165 + 360n + -180n2 = 0 + 180n2 + -180n2
165 + 360n + -180n2 = 180n2 + -180n2

Combine like terms: 180n2 + -180n2 = 0
165 + 360n + -180n2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(11 + 24n + -12n2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(11 + 24n + -12n2)' equal to zero and attempt to solve:

Simplifying
11 + 24n + -12n2 = 0

Solving
11 + 24n + -12n2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-0.9166666667 + -2n + n2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + -2n + 0.9166666667 + n2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + -2n + n2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + -2n + n2 = 0 + 0.9166666667
-2n + n2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
-2n + n2 = 0.9166666667

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 = 0.9166666667 + 1

Reorder the terms:
1 + -2n + n2 = 0.9166666667 + 1

Combine like terms: 0.9166666667 + 1 = 1.9166666667
1 + -2n + n2 = 1.9166666667

Factor a perfect square on the left side:
(n + -1)(n + -1) = 1.9166666667

Calculate the square root of the right side: 1.38443731

Break this problem into two subproblems by setting 
(n + -1) equal to 1.38443731 and -1.38443731.

Subproblem 1
n + -1 = 1.38443731

Simplifying
n + -1 = 1.38443731

Reorder the terms:
-1 + n = 1.38443731

Solving
-1 + n = 1.38443731

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 = 1.38443731 + 1

Combine like terms: -1 + 1 = 0
0 + n = 1.38443731 + 1
n = 1.38443731 + 1

Combine like terms: 1.38443731 + 1 = 2.38443731
n = 2.38443731

Simplifying
n = 2.38443731

Subproblem 2
n + -1 = -1.38443731

Simplifying
n + -1 = -1.38443731

Reorder the terms:
-1 + n = -1.38443731

Solving
-1 + n = -1.38443731

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 = -1.38443731 + 1

Combine like terms: -1 + 1 = 0
0 + n = -1.38443731 + 1
n = -1.38443731 + 1

Combine like terms: -1.38443731 + 1 = -0.38443731
n = -0.38443731

Simplifying
n = -0.38443731

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.38443731, -0.38443731}
Solution
n = {2.38443731, -0.38443731}