Solve (x+4)(x-6)<0

$$( x + 4 ) ( x - 6 ) < 0$$

Solve for x

$$x\in \left(-4,6\right)$$

Solution Steps

For the product to be negative, x+4 and x-6 have to be of the opposite signs. Consider the case when x+4 is positive and x-6 is negative.

$$x+4>0 x-6<0$$

The solution satisfying both inequalities is x\in \left(-4,6\right).

$$x\in \left(-4,6\right)$$

Consider the case when x-6 is positive and x+4 is negative.

$$x-6>0 x+4<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(-4,6\right)$$