Solve for a
a\in \left(0,4\right)
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a\left(a-4\right)<0
Factor out a.
a>0 a-4<0
For the product to be negative, a and a-4 have to be of the opposite signs. Consider the case when a is positive and a-4 is negative.
a\in \left(0,4\right)
The solution satisfying both inequalities is a\in \left(0,4\right).
a-4>0 a<0
Consider the case when a-4 is positive and a is negative.
a\in \emptyset
This is false for any a.
a\in \left(0,4\right)
The final solution is the union of the obtained solutions.
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