(x^2-5)(x^2+1)=0

Solution for (x^2-5)(x^2+1)=0 equation:

Simplifying
(x2 + -5)(x2 + 1) = 0

Reorder the terms:
(-5 + x2)(x2 + 1) = 0

Reorder the terms:
(-5 + x2)(1 + x2) = 0

Multiply (-5 + x2) * (1 + x2)
(-5(1 + x2) + x2(1 + x2)) = 0
((1 * -5 + x2 * -5) + x2(1 + x2)) = 0
((-5 + -5x2) + x2(1 + x2)) = 0
(-5 + -5x2 + (1 * x2 + x2 * x2)) = 0
(-5 + -5x2 + (1x2 + x4)) = 0

Combine like terms: -5x2 + 1x2 = -4x2
(-5 + -4x2 + x4) = 0

Solving
-5 + -4x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x2)(5 + -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 '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {-2.236067978, 2.236067978}