x^4-27x^2+162=0

Solution for x^4-27x^2+162=0 equation:

Simplifying
x4 + -27x2 + 162 = 0

Reorder the terms:
162 + -27x2 + x4 = 0

Solving
162 + -27x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(18 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(18 + -1x2) = 0

Subproblem 1
Set the factor '(18 + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -1x2 = 0

Solving
18 + -1x2 = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x2 = 0 + -18
-1x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-1x2 = -18

Divide each side by '-1'.
x2 = 18

Simplifying
x2 = 18

Take the square root of each side:
x = {-4.242640687, 4.242640687}
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 = {-4.242640687, 4.242640687, -3, 3}