Solve x^2-6x<0

$$x ^ { 2 } - 6 x < 0$$

Solve for x

$$x\in \left(0,6\right)$$

Solution Steps

Factor out x.

$$x\left(x-6\right)<0$$

For the product to be negative, x and x-6 have to be of the opposite signs. Consider the case when x is positive and x-6 is negative.

$$x>0 x-6<0$$

The solution satisfying both inequalities is x\in \left(0,6\right).

$$x\in \left(0,6\right)$$

Consider the case when x-6 is positive and x is negative.

$$x-6>0 x<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(0,6\right)$$