Solve (z+3)(z-3)>0

$$( z + 3 ) ( z - 3 ) > 0$$

Solve for z

$$z\in \left(-\infty,-3\right)\cup \left(3,\infty\right)$$

Solution Steps

For the product to be positive, z+3 and z-3 have to be both negative or both positive. Consider the case when z+3 and z-3 are both negative.

$$z+3<0 z-3<0$$

The solution satisfying both inequalities is z<-3.

$$z<-3$$

Consider the case when z+3 and z-3 are both positive.

$$z-3>0 z+3>0$$

The solution satisfying both inequalities is z>3.

$$z>3$$

The final solution is the union of the obtained solutions.

$$z<-3\text{; }z>3$$