There is a Cubic Formula, but it only works for particular cubics.

You're better off using the remainder and factor theorems to factorise and then using the Null Factor Law.

.

Notice that if you let , you get

.

By the factor and remainder theorems, this means that is a factor.

Now long divide, and you should find

.

So the only solution to this equation is .

P.S. If you're really good with the Binomial Theorem you can see that

by observation...