Solve left(x+3right)left(x-6right)leq0

$$\left( x+3 \right) \left( x-6 \right) \leq 0$$

Solve for x

$$x\in \begin{bmatrix}-3,6\end{bmatrix}$$

Solution Steps

For the product to be ≤0, one of the values x+3 and x-6 has to be ≥0 and the other has to be ≤0. Consider the case when x+3\geq 0 and x-6\leq 0.

$$x+3\geq 0 x-6\leq 0$$

The solution satisfying both inequalities is x\in \left[-3,6\right].

$$x\in \begin{bmatrix}-3,6\end{bmatrix}$$

Consider the case when x+3\leq 0 and x-6\geq 0.

$$x-6\geq 0 x+3\leq 0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \begin{bmatrix}-3,6\end{bmatrix}$$