(x-2)^3*(x+1)(x-1)^2*(x^2+2x+5)<0 inequation

Given the inequality:
$$\left(x - 2\right)^{3} \left(x + 1\right) \left(x - 1\right)^{2} \left(\left(x^{2} + 2 x\right) + 5\right) < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(x - 2\right)^{3} \left(x + 1\right) \left(x - 1\right)^{2} \left(\left(x^{2} + 2 x\right) + 5\right) = 0$$
Solve:
$$x_{1} = -1$$
$$x_{2} = 1$$
$$x_{3} = 2$$
$$x_{4} = -1 - 2 i$$
$$x_{5} = -1 + 2 i$$
Exclude the complex solutions:
$$x_{1} = -1$$
$$x_{2} = 1$$
$$x_{3} = 2$$
This roots
$$x_{1} = -1$$
$$x_{2} = 1$$
$$x_{3} = 2$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-1 + - \frac{1}{10}$$
=
$$- \frac{11}{10}$$
substitute to the expression
$$\left(x - 2\right)^{3} \left(x + 1\right) \left(x - 1\right)^{2} \left(\left(x^{2} + 2 x\right) + 5\right) < 0$$
$$\left(-2 - \frac{11}{10}\right)^{3} \left(- \frac{11}{10} + 1\right) \left(- \frac{11}{10} - 1\right)^{2} \left(\left(\frac{\left(-11\right) 2}{10} + \left(- \frac{11}{10}\right)^{2}\right) + 5\right) < 0$$

5268270231    
---------- < 0
100000000     

but

5268270231    
---------- > 0
100000000     

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

         _____           _____  
        /     \         /
-------ο-------ο-------ο-------
       x1      x2      x3

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -1 \wedge x < 1$$
$$x > 2$$