a^6+4a^4-5a^2=

Solution for a^6+4a^4-5a^2= equation:

Simplifying
a6 + 4a4 + -5a2 = 0

Reorder the terms:
-5a2 + 4a4 + a6 = 0

Solving
-5a2 + 4a4 + a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(-5 + 4a2 + a4) = 0

Factor a trinomial.
a2((-5 + -1a2)(1 + -1a2)) = 0

Factor a difference between two squares.
a2((-5 + -1a2)((1 + a)(1 + -1a))) = 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 '(-5 + -1a2)' equal to zero and attempt to solve:

Simplifying
-5 + -1a2 = 0

Solving
-5 + -1a2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a2 = 0 + 5
-1a2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1a2 = 5

Divide each side by '-1'.
a2 = -5

Simplifying
a2 = -5

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 '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

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

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

Simplifying
a = -1
Subproblem 4
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {0, -1, 1}