3a^2n^2-3a^2n-36a^2=0

Solution for 3a^2n^2-3a^2n-36a^2=0 equation:

Simplifying
3a2n2 + -3a2n + -36a2 = 0

Reorder the terms:
-36a2 + -3a2n + 3a2n2 = 0

Solving
-36a2 + -3a2n + 3a2n2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), '3a2'.
3a2(-12 + -1n + n2) = 0

Factor a trinomial.
3a2((-3 + -1n)(4 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
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 a 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

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

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

Simplifying
0 = 3 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

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

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

Add 'n' to each side of the equation.
-1n + n = -4 + n

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

Simplifying
0 = -4 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}