(z-4)(4z+2)<0 inequation

Given the inequality:
$$\left(z - 4\right) \left(4 z + 2\right) < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(z - 4\right) \left(4 z + 2\right) = 0$$
Solve:
$$x_{1} = -0.5$$
$$x_{2} = 4$$
$$x_{1} = -0.5$$
$$x_{2} = 4$$
This roots
$$x_{1} = -0.5$$
$$x_{2} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-0.5 + - \frac{1}{10}$$
=
$$-0.6$$
substitute to the expression
$$\left(z - 4\right) \left(4 z + 2\right) < 0$$
$$\left(z - 4\right) \left(4 z + 2\right) < 0$$

(-4 + z)*(2 + 4*z) < 0

Then
$$x < -0.5$$
no execute
one of the solutions of our inequality is:
$$x > -0.5 \wedge x < 4$$

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