x^4-36x^2+243=0

Solution for x^4-36x^2+243=0 equation:

Simplifying
x4 + -36x2 + 243 = 0

Reorder the terms:
243 + -36x2 + x4 = 0

Solving
243 + -36x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(27 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(27 + -1x2) = 0

Subproblem 1
Set the factor '(27 + -1x2)' equal to zero and attempt to solve:

Simplifying
27 + -1x2 = 0

Solving
27 + -1x2 = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1x2 = 0 + -27
-1x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-1x2 = -27

Divide each side by '-1'.
x2 = 27

Simplifying
x2 = 27

Take the square root of each side:
x = {-5.196152423, 5.196152423}
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 = {-5.196152423, 5.196152423, -3, 3}