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a+2>0 a-1<0
For the product to be negative, a+2 and a-1 have to be of the opposite signs. Consider the case when a+2 is positive and a-1 is negative.
a\in \left(-2,1\right)
The solution satisfying both inequalities is a\in \left(-2,1\right).
a-1>0 a+2<0
Consider the case when a-1 is positive and a+2 is negative.
a\in \emptyset
This is false for any a.
a\in \left(-2,1\right)
The final solution is the union of the obtained solutions.