27x^2-324=-x^4

Solution for 27x^2-324=-x^4 equation:

Simplifying
27x2 + -324 = -1x4

Reorder the terms:
-324 + 27x2 = -1x4

Solving
-324 + 27x2 = -1x4

Solving for variable 'x'.

Combine like terms: -1x4 + x4 = 0
-324 + 27x2 + x4 = 0

Factor a trinomial.
(-36 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
(-36 + -1x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(-36 + -1x2)' equal to zero and attempt to solve:

Simplifying
-36 + -1x2 = 0

Solving
-36 + -1x2 = 0

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

Add '36' to each side of the equation.
-36 + 36 + -1x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1x2 = 0 + 36
-1x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-1x2 = 36

Divide each side by '-1'.
x2 = -36

Simplifying
x2 = -36

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}