0=x^2(x^4+6x^2-16)

Solution for 0=x^2(x^4+6x^2-16) equation:

Simplifying
0 = x2(x4 + 6x2 + -16)

Reorder the terms:
0 = x2(-16 + 6x2 + x4)
0 = (-16 * x2 + 6x2 * x2 + x4 * x2)
0 = (-16x2 + 6x4 + x6)

Solving
0 = -16x2 + 6x4 + x6

Solving for variable 'x'.
Remove the zero:
16x2 + -6x4 + -1x6 = -16x2 + 6x4 + x6 + 16x2 + -6x4 + -1x6

Reorder the terms:
16x2 + -6x4 + -1x6 = -16x2 + 16x2 + 6x4 + -6x4 + x6 + -1x6

Combine like terms: -16x2 + 16x2 = 0
16x2 + -6x4 + -1x6 = 0 + 6x4 + -6x4 + x6 + -1x6
16x2 + -6x4 + -1x6 = 6x4 + -6x4 + x6 + -1x6

Combine like terms: 6x4 + -6x4 = 0
16x2 + -6x4 + -1x6 = 0 + x6 + -1x6
16x2 + -6x4 + -1x6 = x6 + -1x6

Combine like terms: x6 + -1x6 = 0
16x2 + -6x4 + -1x6 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(16 + -6x2 + -1x4) = 0

Factor a trinomial.
x2((2 + -1x2)(8 + x2)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
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}
Subproblem 3
Set the factor '(8 + x2)' equal to zero and attempt to solve:

Simplifying
8 + x2 = 0

Solving
8 + x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = 0 + -8
x2 = 0 + -8

Combine like terms: 0 + -8 = -8
x2 = -8

Simplifying
x2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0, -1.414213562, 1.414213562}