X(x^2+1)(x^2-4)=0

Solution for X(x^2+1)(x^2-4)=0 equation:

Simplifying
X(x2 + 1)(x2 + -4) = 0

Reorder the terms:
X(1 + x2)(x2 + -4) = 0

Reorder the terms:
X(1 + x2)(-4 + x2) = 0

Multiply (1 + x2) * (-4 + x2)
X(1(-4 + x2) + x2(-4 + x2)) = 0
X((-4 * 1 + x2 * 1) + x2(-4 + x2)) = 0
X((-4 + 1x2) + x2(-4 + x2)) = 0
X(-4 + 1x2 + (-4 * x2 + x2 * x2)) = 0
X(-4 + 1x2 + (-4x2 + x4)) = 0

Combine like terms: 1x2 + -4x2 = -3x2
X(-4 + -3x2 + x4) = 0
(-4 * X + -3x2 * X + x4 * X) = 0
(-4X + -3x2X + x4X) = 0

Solving
-4X + -3x2X + x4X = 0

Solving for variable 'X'.

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

Factor out the Greatest Common Factor (GCF), 'X'.
X(-4 + -3x2 + x4) = 0

Factor a trinomial.
X((-1 + -1x2)(4 + -1x2)) = 0

Factor a difference between two squares.
X((-1 + -1x2)((2 + x)(2 + -1x))) = 0

Subproblem 1
Set the factor 'X' equal to zero and attempt to solve:

Simplifying
X = 0

Solving
X = 0

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

Simplifying
X = 0
Subproblem 2
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

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

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

Simplifying
0 = 1 + x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

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

Simplifying
0 = -2 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 4
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

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

Simplifying
0 = -2 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}