(x^2-2)(x^2+3)=0

Solution for (x^2-2)(x^2+3)=0 equation:

Simplifying
(x2 + -2)(x2 + 3) = 0

Reorder the terms:
(-2 + x2)(x2 + 3) = 0

Reorder the terms:
(-2 + x2)(3 + x2) = 0

Multiply (-2 + x2) * (3 + x2)
(-2(3 + x2) + x2(3 + x2)) = 0
((3 * -2 + x2 * -2) + x2(3 + x2)) = 0
((-6 + -2x2) + x2(3 + x2)) = 0
(-6 + -2x2 + (3 * x2 + x2 * x2)) = 0
(-6 + -2x2 + (3x2 + x4)) = 0

Combine like terms: -2x2 + 3x2 = 1x2
(-6 + 1x2 + x4) = 0

Solving
-6 + 1x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x2)(2 + -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 '(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}