The best approach for this problem is called factoring by grouping.
In this method, the first two terms are one group, and the last two terms are the second group.
Looking at the first group, a factor of x^{2} can be factored out x^{2}(x + 2 ).
Looking at the second group, a factor of -9 can be factored out -9 ( x +2)
Now (this is the good part) it can be noticed that both of these expression have a factor of (x + 2) ,
thus whole expression can be written as
(x + 2) ( x^{2} -9)
Also x^{2} - 9 = (x - 3) (x + 3) , so the original equation is
(x + 2) (x - 3) (x + 3) =0
From this it is easy to see the the solution set is {-3 , -2 ,3 }
The factor by grouping does not always work, but when it does , it works very well and easily.