Solve x^2-15x>0

$${ x }^{ 2 } -15x > 0$$

Solve for x

$$x\in \left(-\infty,0\right)\cup \left(15,\infty\right)$$

Solution Steps

Factor out x.

$$x\left(x-15\right)>0$$

For the product to be positive, x and x-15 have to be both negative or both positive. Consider the case when x and x-15 are both negative.

$$x<0 x-15<0$$

The solution satisfying both inequalities is x<0.

$$x<0$$

Consider the case when x and x-15 are both positive.

$$x-15>0 x>0$$

The solution satisfying both inequalities is x>15.

$$x>15$$

The final solution is the union of the obtained solutions.

$$x<0\text{; }x>15$$