I have a symbolic equation *EQ*, expressed in terms of symbolic variables *d, f, t*. The equation contains a number of 6th degree polynomial roots (with a symbolic coefficient *t*). The equation is quite long and it starts like this:

*EQ = ( d* f* (8*root(z^6 – 12*t*z^5 + (243*t^2*z^4)/8 + (399*t^3*z^3)/4 – (837*t^4*z^2)/2 – (639*t^5*z)/4 + (9945*t^6)/8, z, 1)^5 + 155*t^2*root(z^6 – 12*t*z^5 + (243*t^2*z^4)/8 + (399*t^3*z^3)/4 – (837*t^4*z^2)/2 – (639*t^5*z)/4 + (9945*t^6)/8, z, 1)^3 + ….* and so on

Matlab is unable to solve it with the *solve()* function. My initial thought was that the explicit solution of a polynomial with arbitrary coefficients does not exist (Abel-Ruffini theorem), but I evaluated the expression for a set of numeric variables and then by running regression and guessing the form of the solution I was able to find the exact solution (expressed with symbolic variables *d, f, t*):

*EQ= RegressionConstant * t * d * t*

This puzzles me. If the exact solution does exist, why would Matlab not give it to me straight away? What am I missing?

Thanks for any suggestions