Solve 2a-a^2<0

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

Solve for a

$$a\in \left(-\infty,0\right)\cup \left(2,\infty\right)$$

Solution Steps

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

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

Factor out a.

$$a\left(a-2\right)>0$$

For the product to be positive, a and a-2 have to be both negative or both positive. Consider the case when a and a-2 are both negative.

$$a<0 a-2<0$$

The solution satisfying both inequalities is a<0.

$$a<0$$

Consider the case when a and a-2 are both positive.

$$a-2>0 a>0$$

The solution satisfying both inequalities is a>2.

$$a>2$$

The final solution is the union of the obtained solutions.

$$a<0\text{; }a>2$$