How I can Solve an Advanced Cubic Equation

I am aiming to solve the following cubic equation for x.

x^3*a^2(r-1)+x^2*a*(a-2*(r-1)) - x*(2a+1)+1 = 0

Essentially, I would like to express x as a function of the variable r and a. Any pointer as of how I shouldt ackle this problem. Thanks

[Walter Roberson]

Symbolic Toolbox solve() with 'MaxDegree', 3 option and simplify() afterwards.

Complete answers exist, but it is normal for the output to be what appears to be a moderately long string of nonsense.

[J. Alex Lee]

Why not just start with Wikipedia or textbooks on solution of cubics? It's usually easier to do that than to decipher/simplify the results of symbolic solvers (at least my experience with Mathematica; I've never use TMW's symbolic toolbox)

Answer 1

[Walter Roberson]

syms x a r
eqn = x^3*a^2*(r-1)+x^2*a*(a-2*(r-1)) - x*(2*a+1)+1;
sol = simplify(solve(eqn, x, 'maxdegree', 3));

The second and third solution are over 1000 characters each. I don't think the solution will have any meaning to you.