a^4+2a^2+a^2=0

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

Simplifying
a4 + 2a2 + a2 = 0

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

Combine like terms: 2a2 + a2 = 3a2
3a2 + a4 = 0

Solving
3a2 + a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(3 + a2) = 0

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 + a2)' equal to zero and attempt to solve:

Simplifying
3 + a2 = 0

Solving
3 + a2 = 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 + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a2 = 0 + -3
a2 = 0 + -3

Combine like terms: 0 + -3 = -3
a2 = -3

Simplifying
a2 = -3

The solution to this equation could not be determined.

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