5a^4-3a^2=2

Solution for 5a^4-3a^2=2 equation:

Simplifying
5a4 + -3a2 = 2

Reorder the terms:
-3a2 + 5a4 = 2

Solving
-3a2 + 5a4 = 2

Solving for variable 'a'.

Reorder the terms:
-2 + -3a2 + 5a4 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -3a2 + 5a4 = 0

Factor a trinomial.
(-2 + -5a2)(1 + -1a2) = 0

Factor a difference between two squares.
(-2 + -5a2)((1 + a)(1 + -1a)) = 0

Subproblem 1
Set the factor '(-2 + -5a2)' equal to zero and attempt to solve:

Simplifying
-2 + -5a2 = 0

Solving
-2 + -5a2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5a2 = 0 + 2
-5a2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5a2 = 2

Divide each side by '-5'.
a2 = -0.4

Simplifying
a2 = -0.4

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 '(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 = {-1, 1}