Solve x^2+3x^<0

$${ x }^{ 2 } +3 { x }^{ } < 0$$

Solve for x

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

Solution Steps

Calculate x to the power of 1 and get x.

$$x^{2}+3x<0$$

Factor out x.

$$x\left(x+3\right)<0$$

For the product to be negative, x+3 and x have to be of the opposite signs. Consider the case when x+3 is positive and x is negative.

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

The solution satisfying both inequalities is x\in \left(-3,0\right).

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

Consider the case when x is positive and x+3 is negative.

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

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

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