First we solve the left inequality:
We use the chart method to determine signs, dividing points (the zero points of the linear factors) are x = 0 and x = −1/2.
So the first and the third interval form the solution to this inequality,
when we try to substitute the dividing points, we see that
Next we solve the right inequality:
This time the chart method is not even necessary, the solution to this inequality is clearly (−∞,0).
The solution to the whole problem is obtained by intersecting the two sets we obtained, that is,