z^2+5*z<0 inequation

Given the inequality:
$$z^{2} + 5 z < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$z^{2} + 5 z = 0$$
Solve:
$$x_{1} = -5$$
$$x_{2} = 0$$
$$x_{1} = -5$$
$$x_{2} = 0$$
This roots
$$x_{1} = -5$$
$$x_{2} = 0$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-5 + - \frac{1}{10}$$
=
$$-5.1$$
substitute to the expression
$$z^{2} + 5 z < 0$$
$$z^{2} + 5 z < 0$$

 2          
z  + 5*z < 0
    

Then
$$x < -5$$
no execute
one of the solutions of our inequality is:
$$x > -5 \wedge x < 0$$

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