0=x^8-162-79x^4

Solution for 0=x^8-162-79x^4 equation:

Simplifying
0 = x8 + -162 + -79x4

Reorder the terms:
0 = -162 + -79x4 + x8

Solving
0 = -162 + -79x4 + x8

Solving for variable 'x'.

Combine like terms: 0 + 162 = 162
162 + 79x4 + -1x8 = -162 + -79x4 + x8 + 162 + 79x4 + -1x8

Reorder the terms:
162 + 79x4 + -1x8 = -162 + 162 + -79x4 + 79x4 + x8 + -1x8

Combine like terms: -162 + 162 = 0
162 + 79x4 + -1x8 = 0 + -79x4 + 79x4 + x8 + -1x8
162 + 79x4 + -1x8 = -79x4 + 79x4 + x8 + -1x8

Combine like terms: -79x4 + 79x4 = 0
162 + 79x4 + -1x8 = 0 + x8 + -1x8
162 + 79x4 + -1x8 = x8 + -1x8

Combine like terms: x8 + -1x8 = 0
162 + 79x4 + -1x8 = 0

Factor a trinomial.
(81 + -1x4)(2 + x4) = 0

Factor a difference between two squares.
((9 + x2)(9 + -1x2))(2 + x4) = 0

Factor a difference between two squares.
((9 + x2)((3 + x)(3 + -1x)))(2 + x4) = 0

Subproblem 1
Set the factor '(2 + x4)' equal to zero and attempt to solve:

Simplifying
2 + x4 = 0

Solving
2 + x4 = 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 + x4 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x4 = 0 + -2
x4 = 0 + -2

Combine like terms: 0 + -2 = -2
x4 = -2

Simplifying
x4 = -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 '(9 + x2)' equal to zero and attempt to solve:

Simplifying
9 + x2 = 0

Solving
9 + x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = 0 + -9
x2 = 0 + -9

Combine like terms: 0 + -9 = -9
x2 = -9

Simplifying
x2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
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 4
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}