x^4-12x^2-45=0

Solution for x^4-12x^2-45=0 equation:

Simplifying
x4 + -12x2 + -45 = 0

Reorder the terms:
-45 + -12x2 + x4 = 0

Solving
-45 + -12x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x2)(15 + -1x2) = 0

Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x2 = 0

Solving
-3 + -1x2 = 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 + -1x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x2 = 0 + 3
-1x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x2 = 3

Divide each side by '-1'.
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.
Subproblem 2
Set the factor '(15 + -1x2)' equal to zero and attempt to solve:

Simplifying
15 + -1x2 = 0

Solving
15 + -1x2 = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x2 = 0 + -15
-1x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-1x2 = -15

Divide each side by '-1'.
x2 = 15

Simplifying
x2 = 15

Take the square root of each side:
x = {-3.872983346, 3.872983346}
Solution
x = {-3.872983346, 3.872983346}