Solve the inequality (x+3)(2x-3)

We'll conclude that a product is negative if the factors
are of opposite sign.

There are 2 cases of
study:

1)  (2x-3) <
0

and

      (x+3) >
0

We'll solve the first inequality. For this reason, we'll
isolate 2x to the left side.

2x <
3

We'll divide by 2:

x
< 3/2

We'll solve  the 2nd
inequality:

    (x+3) >
0

We'll subtract 3 both
sides:

x > -3

The
common solution of the first system of inequalities is the interval (-3 ,
3/2).

We'll solve the second case  for the following system
of inequalities:

2)  (2x-3) >
0

and

      (x+3) <
0

2x-3 > 0

We'll add 3
both sides:

2x > 3

x
> 3/2

     (x+3) <
0

x < -3

Since there is
not a common interval to satisfy both inequalities, we don't have a solution for the 2nd
case.

So, the complete solution is the
solution from the first system of inequalities, namely the interval (-3 ,
3/2).