Find the Characteristic root of the matrix
I take it that you are worried about the cubic nature of the polynomial and you dont know how to solve cubics.
In this particular case, observe that if you expand the determinant as:
Now observe that is a factor of all the three  terms.
I hope you can finish it now
Why did you write as ? When you want to find a root for a polynomial, you want to factor it completely. You cant leave terms like + 1 hanging in the equality.
Note: You want factor it completely because you know that the product of 2 real numbers is 0 means at least one of them is 0.