I am learning math (calculus) by myself and for one specific exercise I have to solve a set of equations. I try to do it without any digital tools, but the task seems very daunting to me, so I am wondering: what is the most time-efficient way to solve this set of equations? My "normal" strategy would be to simply write it all out until I can write certain variables in terms of other variables and fill in that result. This is it:
$A(t-1)^2(t+1)^2+B(t-1)(t+1)^2+C(t+1)^2+D(t-1)^3(t+1)+E(t-1)^3=1$
This will give us a function of $t^4$ which is $0$, a function of $t^3$ also $0$, a function of $t^2$ also $0$, a function of $t$ also $0$ and a function of constants which is $1$.
The task seems rather daunting to me. So what is the most efficient way to solve this set of equations without use of digital tools?
Thanks!
PS, any jokes about lacking willpower are also most welcome