Solve (s+3)(s-4)>0

$$( s + 3 ) ( s - 4 ) > 0$$

Solve for s

$$s\in \left(-\infty,-3\right)\cup \left(4,\infty\right)$$

Solution Steps

For the product to be positive, s+3 and s-4 have to be both negative or both positive. Consider the case when s+3 and s-4 are both negative.

$$s+3<0 s-4<0$$

The solution satisfying both inequalities is s<-3.

$$s<-3$$

Consider the case when s+3 and s-4 are both positive.

$$s-4>0 s+3>0$$

The solution satisfying both inequalities is s>4.

$$s>4$$

The final solution is the union of the obtained solutions.

$$s<-3\text{; }s>4$$