Exponential/Polynomial Hybrid Expression??

Hello, I seem to have hit a stumbling block that unless I have missed something obvious, does not have an elementary solution. I have the following expressions:

-6e^(t(c-d)) + ((c-d)^3)t^3 + 3((c-d)^2)t^2 + 6(c-d)t + 6 = 0

and similarly,

-6e^(t(c-d)) + ((c-d)^3)t^3 + 3((c-d)^2)t^2 + 6(c-d)t + 6 = 6b(14 + b)

Note that b, c and d are known constants (they are probability values). Additionally, I am sure that the two expressions use the same method to solve. However, I am not even sure that this expression is solvable for t, which is what I am trying to do. Any insight or guidance would be greatly appreciated, thanks!

-A puzzled math student