2a^4+2a^2-180=0

Solution for 2a^4+2a^2-180=0 equation:

Simplifying
2a4 + 2a2 + -180 = 0

Reorder the terms:
-180 + 2a2 + 2a4 = 0

Solving
-180 + 2a2 + 2a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + a2 + a4) = 0

Factor a trinomial.
2((-10 + -1a2)(9 + -1a2)) = 0

Factor a difference between two squares.
2((-10 + -1a2)((3 + a)(3 + -1a))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -1a2)' equal to zero and attempt to solve:

Simplifying
-10 + -1a2 = 0

Solving
-10 + -1a2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1a2 = 0 + 10
-1a2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1a2 = 10

Divide each side by '-1'.
a2 = -10

Simplifying
a2 = -10

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

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

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

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

Simplifying
a = 3
Solution
a = {-3, 3}