Solve for x
x\in \left(-3,0\right)
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3x\left(x+3\right)<0
Factor out x.
x+3>0 x<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\in \left(-3,0\right)
The solution satisfying both inequalities is x\in \left(-3,0\right).
x>0 x+3<0
Consider the case when x is positive and x+3 is negative.
x\in \emptyset
This is false for any x.
x\in \left(-3,0\right)
The final solution is the union of the obtained solutions.
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