Solve x^2<-6x

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

Solve for x

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

Solution Steps

Add 6x to both sides.

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

Factor out x.

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

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

$$x+6>0 x<0$$

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

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

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

$$x>0 x+6<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

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