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 −1/2 satisfies the inequality, so it should be included, while 1 does not. Conclusion: The left inequality has the solution

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,