14*x^6-14*x^4<0 inequation

Given the inequality:
$$14 x^{6} - 14 x^{4} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$14 x^{6} - 14 x^{4} = 0$$
Solve:
Given the equation
$$14 x^{6} - 14 x^{4} = 0$$
Obviously:

x0 = 0

next,
transform
$$\frac{1}{x^{2}} = 1$$
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:
$$\frac{1}{\sqrt{\frac{1}{x^{2}}}} = \frac{1}{\sqrt{1}}$$
$$\frac{1}{\sqrt{\frac{1}{x^{2}}}} = \left(-1\right) \frac{1}{\sqrt{1}}$$
or
$$x = 1$$
$$x = -1$$
We get the answer: x = 1
We get the answer: x = -1
or
$$x_{1} = -1$$
$$x_{2} = 1$$

$$x_{1} = 1$$
$$x_{2} = -1$$
$$x_{1} = 1$$
$$x_{2} = -1$$
This roots
$$x_{2} = -1$$
$$x_{1} = 1$$
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
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-1 + - \frac{1}{10}$$
=
$$- \frac{11}{10}$$
substitute to the expression
$$14 x^{6} - 14 x^{4} < 0$$
$$- 14 \left(- \frac{11}{10}\right)^{4} + 14 \left(- \frac{11}{10}\right)^{6} < 0$$

2152227    
------- < 0
 500000    

but

2152227    
------- > 0
 500000    

Then
$$x < -1$$
no execute
one of the solutions of our inequality is:
$$x > -1 \wedge x < 1$$

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