Solve for m
m\in \left(0,\frac{1}{9}\right)
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4m\left(9m-1\right)<0
Factor out m.
m>0 m-\frac{1}{9}<0
For the product to be negative, m and m-\frac{1}{9} have to be of the opposite signs. Consider the case when m is positive and m-\frac{1}{9} is negative.
m\in \left(0,\frac{1}{9}\right)
The solution satisfying both inequalities is m\in \left(0,\frac{1}{9}\right).
m-\frac{1}{9}>0 m<0
Consider the case when m-\frac{1}{9} is positive and m is negative.
m\in \emptyset
This is false for any m.
m\in \left(0,\frac{1}{9}\right)
The final solution is the union of the obtained solutions.
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