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x+2<0 3-x<0
For the product to be positive, x+2 and 3-x have to be both negative or both positive. Consider the case when x+2 and 3-x are both negative.
x\in \emptyset
This is false for any x.
3-x>0 x+2>0
Consider the case when x+2 and 3-x are both positive.
x\in \left(-2,3\right)
The solution satisfying both inequalities is x\in \left(-2,3\right).
x\in \left(-2,3\right)
The final solution is the union of the obtained solutions.