Solve (x+2)(x+4)>0

$$( x + 2 ) ( x + 4 ) > 0$$

Solve for x

$$x\in \left(-\infty,-4\right)\cup \left(-2,\infty\right)$$

Solution Steps

For the product to be positive, x+4 and x+2 have to be both negative or both positive. Consider the case when x+4 and x+2 are both negative.

$$x+4<0 x+2<0$$

The solution satisfying both inequalities is x<-4.

$$x<-4$$

Consider the case when x+4 and x+2 are both positive.

$$x+2>0 x+4>0$$

The solution satisfying both inequalities is x>-2.

$$x>-2$$

The final solution is the union of the obtained solutions.

$$x<-4\text{; }x>-2$$