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