Solve 4x(x+3)>0

$$4 x ( x + 3 ) > 0$$

Solve for x

$$x\in \left(-\infty,-3\right)\cup \left(0,\infty\right)$$

Solution Steps

Use the distributive property to multiply 4x by x+3.

$$4x^{2}+12x>0$$

Factor out x.

$$4x\left(x+3\right)>0$$

For the product to be positive, x+3 and x have to be both negative or both positive. Consider the case when x+3 and x are both negative.

$$x+3<0 x<0$$

The solution satisfying both inequalities is x<-3.

$$x<-3$$

Consider the case when x+3 and x are both positive.

$$x>0 x+3>0$$

The solution satisfying both inequalities is x>0.

$$x>0$$

The final solution is the union of the obtained solutions.

$$x<-3\text{; }x>0$$