-x^4+72x^2+225=0

Solution for -x^4+72x^2+225=0 equation:

Simplifying
-1x4 + 72x2 + 225 = 0

Reorder the terms:
225 + 72x2 + -1x4 = 0

Solving
225 + 72x2 + -1x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(75 + -1x2)(3 + x2) = 0

Subproblem 1
Set the factor '(75 + -1x2)' equal to zero and attempt to solve:

Simplifying
75 + -1x2 = 0

Solving
75 + -1x2 = 0

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

Add '-75' to each side of the equation.
75 + -75 + -1x2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -1x2 = 0 + -75
-1x2 = 0 + -75

Combine like terms: 0 + -75 = -75
-1x2 = -75

Divide each side by '-1'.
x2 = 75

Simplifying
x2 = 75

Take the square root of each side:
x = {-8.660254038, 8.660254038}
Subproblem 2
Set the factor '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

Solving
3 + x2 = 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 + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x2 = 0 + -3
x2 = 0 + -3

Combine like terms: 0 + -3 = -3
x2 = -3

Simplifying
x2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-8.660254038, 8.660254038}