Find the zeros of the left side, which will be the
critical numbers for the inequality:



Draw a number line with the critical numbers marked.
Note that , so we mark a point about
2/3rds of the way between 1 and 2.

We can go ahead and mark them with darkened circles
since the inequality has  not .

-----------●-----------------●------------
-4   -3   -2   -1    0    1    2    3    4 

That identifies three intervals, (-∞,-2], [-2,5/3], [2,∞)

We choose an easy test point, an interior point of each
interval.

interval |test pt.  |sign of (3x-5)(x+2) |include in solution?|
(-∞,-2]  |  x=-3    |     +              |      yes           |
[-2,5/3] |  x=0     |     -              |       no           |
  [2,∞)  |  x=3     |     +              |      yes           |

So the number line graph is

<==========●-----------------●===========>
-4   -3   -2   -1    0    1    2    3    4 

And so the solution is (-∞,-2] U [5/3,∞)

Edwin