solve the differential equation $2y^{(5)}-7y^{(4)}+12y'''-8y''=0$. I cannot find the roots of the characteristic equation to get a solution.  I only know the basic way to solve these equations.  I factored out an $r^2$.
$2r^5-7r^4+12r^3-8r^2 = 0$
$r^2(2r^3-7r^2+12r-8) = 0$

Check Wolfram alpha for further factorization.
https://www.wolframalpha.com/input/?i=2x%5E3-7x%5E2%2B12x-8%3D0&lk=4&num=2
Are you sure you have all signs right? Also the other answer?!
