Solve (x-15)(2x+42)>0

$$( x - 15 ) ( 2 x + 42 ) > 0$$

Solve for x

$$x\in \left(-\infty,-21\right)\cup \left(15,\infty\right)$$

Solution Steps

For the product to be positive, 2x+42 and x-15 have to be both negative or both positive. Consider the case when 2x+42 and x-15 are both negative.

$$2x+42<0 x-15<0$$

The solution satisfying both inequalities is x<-21.

$$x<-21$$

Consider the case when 2x+42 and x-15 are both positive.

$$x-15>0 2x+42>0$$

The solution satisfying both inequalities is x>15.

$$x>15$$

The final solution is the union of the obtained solutions.

$$x<-21\text{; }x>15$$