2a^4-32=0

Solution for 2a^4-32=0 equation:

Simplifying
2a4 + -32 = 0

Reorder the terms:
-32 + 2a4 = 0

Solving
-32 + 2a4 = 0

Solving for variable 'a'.

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

Add '32' to each side of the equation.
-32 + 32 + 2a4 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 2a4 = 0 + 32
2a4 = 0 + 32

Combine like terms: 0 + 32 = 32
2a4 = 32

Divide each side by '2'.
a4 = 16

Simplifying
a4 = 16

Reorder the terms:
-16 + a4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + a4 = 0

Factor a difference between two squares.
(4 + a2)(-4 + a2) = 0

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

Subproblem 1
Set the factor '(4 + a2)' equal to zero and attempt to solve:

Simplifying
4 + a2 = 0

Solving
4 + a2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a2 = 0 + -4
a2 = 0 + -4

Combine like terms: 0 + -4 = -4
a2 = -4

Simplifying
a2 = -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 '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 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 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Subproblem 3
Set the factor '(-2 + a)' equal to zero and attempt to solve:

Simplifying
-2 + a = 0

Solving
-2 + a = 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 + a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + a = 0 + 2
a = 0 + 2

Combine like terms: 0 + 2 = 2
a = 2

Simplifying
a = 2
Solution
a = {-2, 2}