Finding the Range for r in an Inequality: Tips and Tricks

[azdang]

I'm working on a problem in which I have to find a range for r. I have an upper bound on it, but I can't seem to get the lower bound.

Here is the inequality to start with:
\lambdar - r³ + \lambda < 0

Eventually, I get it down to:
\lambda < \frac{r^3}{r+1}

However, I need r by itself on one side, and I have no idea what to do. Is there anything I actually could do or am I stuck?

Another note: r>0 and \lambda>0. Thanks!

 

[Focus]

You need to solve \lambda r -r^3+\lambda=0 first.