Solve -m^2+2m>0

$$- m ^ { 2 } + 2 m > 0$$

Solve for m

$$m\in \left(0,2\right)$$

Solution Steps

Multiply the inequality by -1 to make the coefficient of the highest power in -m^{2}+2m positive. Since -1 is negative, the inequality direction is changed.

$$m^{2}-2m<0$$

Factor out m.

$$m\left(m-2\right)<0$$

For the product to be negative, m and m-2 have to be of the opposite signs. Consider the case when m is positive and m-2 is negative.

$$m>0 m-2<0$$

The solution satisfying both inequalities is m\in \left(0,2\right).

$$m\in \left(0,2\right)$$

Consider the case when m-2 is positive and m is negative.

$$m-2>0 m<0$$

This is false for any m.

$$m\in \emptyset$$

The final solution is the union of the obtained solutions.

$$m\in \left(0,2\right)$$