x^4-12x^2-13=0

Solution for x^4-12x^2-13=0 equation:

Simplifying
x4 + -12x2 + -13 = 0

Reorder the terms:
-13 + -12x2 + x4 = 0

Solving
-13 + -12x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x2)(13 + -1x2) = 0

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

Simplifying
-1 + -1x2 = 0

Solving
-1 + -1x2 = 0

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

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

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

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

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

Simplifying
x2 = -1

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 '(13 + -1x2)' equal to zero and attempt to solve:

Simplifying
13 + -1x2 = 0

Solving
13 + -1x2 = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x2 = 0 + -13
-1x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-1x2 = -13

Divide each side by '-1'.
x2 = 13

Simplifying
x2 = 13

Take the square root of each side:
x = {-3.605551275, 3.605551275}
Solution
x = {-3.605551275, 3.605551275}