Solve c^2-c>0

$$c ^ { 2 } - c > 0$$

Solve for c

$$c\in \left(-\infty,0\right)\cup \left(1,\infty\right)$$

Solution Steps

Factor out c.

$$c\left(c-1\right)>0$$

For the product to be positive, c and c-1 have to be both negative or both positive. Consider the case when c and c-1 are both negative.

$$c<0 c-1<0$$

The solution satisfying both inequalities is c<0.

$$c<0$$

Consider the case when c and c-1 are both positive.

$$c-1>0 c>0$$

The solution satisfying both inequalities is c>1.

$$c>1$$

The final solution is the union of the obtained solutions.

$$c<0\text{; }c>1$$