5c²-5c(c+5)≤100 inequation

Given the inequality:
$$5 c^{2} - 5 c \left(c + 5\right) \leq 100$$
To solve this inequality, we must first solve the corresponding equation:
$$5 c^{2} - 5 c \left(c + 5\right) = 100$$
Solve:
$$x_{1} = -4$$
$$x_{1} = -4$$
This roots
$$x_{1} = -4$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-4 + - \frac{1}{10}$$
=
$$-4.1$$
substitute to the expression
$$5 c^{2} - 5 c \left(c + 5\right) \leq 100$$
$$5 c^{2} - 5 c \left(c + 5\right) \leq 100$$

   2                     
5*c  - 5*c*(5 + c) <= 100
       

Then
$$x \leq -4$$
no execute
the solution of our inequality is:
$$x \geq -4$$

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