0=x^4-8x^2-9

Solution for 0=x^4-8x^2-9 equation:

Simplifying
0 = x4 + -8x2 + -9

Reorder the terms:
0 = -9 + -8x2 + x4

Solving
0 = -9 + -8x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 9 = 9
9 + 8x2 + -1x4 = -9 + -8x2 + x4 + 9 + 8x2 + -1x4

Reorder the terms:
9 + 8x2 + -1x4 = -9 + 9 + -8x2 + 8x2 + x4 + -1x4

Combine like terms: -9 + 9 = 0
9 + 8x2 + -1x4 = 0 + -8x2 + 8x2 + x4 + -1x4
9 + 8x2 + -1x4 = -8x2 + 8x2 + x4 + -1x4

Combine like terms: -8x2 + 8x2 = 0
9 + 8x2 + -1x4 = 0 + x4 + -1x4
9 + 8x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
9 + 8x2 + -1x4 = 0

Factor a trinomial.
(9 + -1x2)(1 + x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(1 + x2) = 0

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

Simplifying
1 + x2 = 0

Solving
1 + x2 = 0

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

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

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

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

Simplifying
x2 = -1

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3, 3}