(X^2-9)(X^2+2)=0

Solution for (X^2-9)(X^2+2)=0 equation:

Simplifying
(X2 + -9)(X2 + 2) = 0

Reorder the terms:
(-9 + X2)(X2 + 2) = 0

Reorder the terms:
(-9 + X2)(2 + X2) = 0

Multiply (-9 + X2) * (2 + X2)
(-9(2 + X2) + X2(2 + X2)) = 0
((2 * -9 + X2 * -9) + X2(2 + X2)) = 0
((-18 + -9X2) + X2(2 + X2)) = 0
(-18 + -9X2 + (2 * X2 + X2 * X2)) = 0
(-18 + -9X2 + (2X2 + X4)) = 0

Combine like terms: -9X2 + 2X2 = -7X2
(-18 + -7X2 + X4) = 0

Solving
-18 + -7X2 + X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(-2 + -1X2)(9 + -1X2) = 0

Factor a difference between two squares.
(-2 + -1X2)((3 + X)(3 + -1X)) = 0

Subproblem 1
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

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 '(3 + X)' equal to zero and attempt to solve:

Simplifying
3 + X = 0

Solving
3 + X = 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 + X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + X = 0 + -3
X = 0 + -3

Combine like terms: 0 + -3 = -3
X = -3

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

Simplifying
3 + -1X = 0

Solving
3 + -1X = 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 + -1X = 0 + -3

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

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

Divide each side by '-1'.
X = 3

Simplifying
X = 3
Solution
X = {-3, 3}