x^4-14x^2-32=0

Solution for x^4-14x^2-32=0 equation:

Simplifying
x4 + -14x2 + -32 = 0

Reorder the terms:
-32 + -14x2 + x4 = 0

Solving
-32 + -14x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
(-2 + -1x2)((4 + x)(4 + -1x)) = 0

Subproblem 1
Set the factor '(-2 + -1x2)' equal to zero and attempt to solve:

Simplifying
-2 + -1x2 = 0

Solving
-2 + -1x2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x2 = 0 + 2
-1x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1x2 = 2

Divide each side by '-1'.
x2 = -2

Simplifying
x2 = -2

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4
Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-4, 4}