a^4-6a^2+5=0

Solution for a^4-6a^2+5=0 equation:

Simplifying
a4 + -6a2 + 5 = 0

Reorder the terms:
5 + -6a2 + a4 = 0

Solving
5 + -6a2 + a4 = 0

Solving for variable 'a'.

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

Factor a difference between two squares.
((1 + a)(1 + -1a))(5 + -1a2) = 0

Subproblem 1
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

Take the square root of each side:
a = {-2.236067978, 2.236067978}
Subproblem 2
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 3
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 = {-2.236067978, 2.236067978, -1, 1}