I tried this several ways, and always found myself having to solve a quartic equation, so I thought I was stuck.
I finally realized it can be solved if you recognize a negative value of x that produces a minimum (and therefore a solution of that quartic), then use division to obtain a simple cubic you can solve. The result agrees with what I found using GeoGebra.
Where does this problem come from? It isn't exactly easy ... nor is it just an algebra problem, as I needed calculus.