find all values of x: (x+1)(x-3)^2(2x-1) greater than or equal to 0
1) You have three breaks in the Real Numbers. x = -1, x = 3, and x = 1/2. Simply try a value in each of the four regions so defined and you are done.
2) Notice that (x-3)^2 is never negative. The only way for this expression to be positive is for (x+1) and (2x-1) to have the same sign. Where is that?
In both cases, you will want to include the three break points, as the question includes "=0".