(x^2+16)(x^2-4)=0

Solution for (x^2+16)(x^2-4)=0 equation:

Simplifying
(x2 + 16)(x2 + -4) = 0

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

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

Multiply (16 + x2) * (-4 + x2)
(16(-4 + x2) + x2(-4 + x2)) = 0
((-4 * 16 + x2 * 16) + x2(-4 + x2)) = 0
((-64 + 16x2) + x2(-4 + x2)) = 0
(-64 + 16x2 + (-4 * x2 + x2 * x2)) = 0
(-64 + 16x2 + (-4x2 + x4)) = 0

Combine like terms: 16x2 + -4x2 = 12x2
(-64 + 12x2 + x4) = 0

Solving
-64 + 12x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-16 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-16 + -1x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(-16 + -1x2)' equal to zero and attempt to solve:

Simplifying
-16 + -1x2 = 0

Solving
-16 + -1x2 = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x2 = 0 + 16
-1x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1x2 = 16

Divide each side by '-1'.
x2 = -16

Simplifying
x2 = -16

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 + 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

Simplifying
x = -2
Subproblem 3
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

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

Simplifying
x = 2
Solution
x = {-2, 2}