Solve (x-6)(x-14)>0

$$( x - 6 ) ( x - 14 ) > 0$$

Solve for x

$$x\in \left(-\infty,6\right)\cup \left(14,\infty\right)$$

Solution Steps

For the product to be positive, x-6 and x-14 have to be both negative or both positive. Consider the case when x-6 and x-14 are both negative.

$$x-6<0 x-14<0$$

The solution satisfying both inequalities is x<6.

$$x<6$$

Consider the case when x-6 and x-14 are both positive.

$$x-14>0 x-6>0$$

The solution satisfying both inequalities is x>14.

$$x>14$$

The final solution is the union of the obtained solutions.

$$x<6\text{; }x>14$$