I am curious to know which values of $t \gt 0$ solve the following equation in terms of the constants $a,b,c$.
$a e^{-2 b t} - e^{-2 t} + c e^{-3 b t} + c e ^{- 3 t} = 0$
where
$a \gt 1, b \gt 1, c \gt 0, t \gt 0$.
I would like to know how many roots it has, depending on the values of the constants, and to know the formulas for these roots in terms of the constants, if possible.