x^8-64x^6<0 inequation

Given the inequality:
$$x^{8} - 64 x^{6} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x^{8} - 64 x^{6} = 0$$
Solve:
Given the equation
$$x^{8} - 64 x^{6} = 0$$
Obviously:

x0 = 0

next,
transform
$$x^{2} = 64$$
Because equation degree is equal to = 2 - contains the even number 2 in the numerator, then
the equation has two real roots.
Get the root 2-th degree of the equation sides:
We get:
$$\sqrt{x^{2}} = \sqrt{64}$$
$$\sqrt{x^{2}} = \left(-1\right) \sqrt{64}$$
or
$$x = 8$$
$$x = -8$$
We get the answer: x = 8
We get the answer: x = -8
or
$$x_{1} = -8$$
$$x_{2} = 8$$

$$x_{1} = 8$$
$$x_{2} = -8$$
$$x_{1} = 8$$
$$x_{2} = -8$$
This roots
$$x_{2} = -8$$
$$x_{1} = 8$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-8 + - \frac{1}{10}$$
=
$$- \frac{81}{10}$$
substitute to the expression
$$x^{8} - 64 x^{6} < 0$$
$$- 64 \left(- \frac{81}{10}\right)^{6} + \left(- \frac{81}{10}\right)^{8} < 0$$

45471155373441    
-------------- < 0
  100000000       

but

45471155373441    
-------------- > 0
  100000000       

Then
$$x < -8$$
no execute
one of the solutions of our inequality is:
$$x > -8 \wedge x < 8$$

         _____  
        /     \  
-------ο-------ο-------
       x2      x1