180(n-2)=20n*n

Solution for 180(n-2)=20n*n equation:

Simplifying
180(n + -2) = 20n * n

Reorder the terms:
180(-2 + n) = 20n * n
(-2 * 180 + n * 180) = 20n * n
(-360 + 180n) = 20n * n

Multiply n * n
-360 + 180n = 20n2

Solving
-360 + 180n = 20n2

Solving for variable 'n'.

Combine like terms: 20n2 + -20n2 = 0
-360 + 180n + -20n2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-18 + 9n + -1n2) = 0

Factor a trinomial.
20((-6 + n)(3 + -1n)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-6 + n)' equal to zero and attempt to solve:

Simplifying
-6 + n = 0

Solving
-6 + n = 0

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

Add '6' to each side of the equation.
-6 + 6 + n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + n = 0 + 6
n = 0 + 6

Combine like terms: 0 + 6 = 6
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {6, 3}