Suggestion for solving is to try to look for binomial factorization for the cubic polynomial. Try dividing by (x-1), (x+1), (x-2), and (x+2). At least one of them should give no remainder. The ones which divide giving no remainder are binomial factors.
Now, I tried it myself. x+1 is the only binomial factor. , so when you try to use the general solution for a quadratic equation to find roots of the quadratic expression, you will only find the complex roots, and . the only real root then for the given cubic equation is .