Solve (x+3)(x-2)leq0

$$( x + 3 ) ( x - 2 ) \leq 0$$

Solve for x

$$x\in \begin{bmatrix}-3,2\end{bmatrix}$$

Solution Steps

For the product to be ≤0, one of the values x+3 and x-2 has to be ≥0 and the other has to be ≤0. Consider the case when x+3\geq 0 and x-2\leq 0.

$$x+3\geq 0 x-2\leq 0$$

The solution satisfying both inequalities is x\in \left[-3,2\right].

$$x\in \begin{bmatrix}-3,2\end{bmatrix}$$

Consider the case when x+3\leq 0 and x-2\geq 0.

$$x-2\geq 0 x+3\leq 0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \begin{bmatrix}-3,2\end{bmatrix}$$