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

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

Simplifying
(x2 + -2)(x2 + 1) = 0

Reorder the terms:
(-2 + x2)(x2 + 1) = 0

Reorder the terms:
(-2 + x2)(1 + x2) = 0

Multiply (-2 + x2) * (1 + x2)
(-2(1 + x2) + x2(1 + x2)) = 0
((1 * -2 + x2 * -2) + x2(1 + x2)) = 0
((-2 + -2x2) + x2(1 + x2)) = 0
(-2 + -2x2 + (1 * x2 + x2 * x2)) = 0
(-2 + -2x2 + (1x2 + x4)) = 0

Combine like terms: -2x2 + 1x2 = -1x2
(-2 + -1x2 + x4) = 0

Solving
-2 + -1x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x2)(2 + -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 '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {-1.414213562, 1.414213562}