Solve left(x+2right)left(x-1right)>0

$$\left( x+2 \right) \left( x-1 \right) > 0$$

Solve for x

$$x\in \left(-\infty,-2\right)\cup \left(1,\infty\right)$$

Solution Steps

For the product to be positive, x+2 and x-1 have to be both negative or both positive. Consider the case when x+2 and x-1 are both negative.

$$x+2<0 x-1<0$$

The solution satisfying both inequalities is x<-2.

$$x<-2$$

Consider the case when x+2 and x-1 are both positive.

$$x-1>0 x+2>0$$

The solution satisfying both inequalities is x>1.

$$x>1$$

The final solution is the union of the obtained solutions.

$$x<-2\text{; }x>1$$