How to Solve a Complex Cubic Equation?

Questions
1

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 should tackle this problem. Thanks

2

Try

Solve[{x^3 a^2 (r - 1) + x^2 a (a - 2 (r - 1)) - x*(2 a + 1) + 1 == 0}, x]