Consider the bases $b=(p_1, p_2)$ and $b' = (q_1, q_2)$ for $p_1$, where $p_1 = 6 + 3x$, $p_2 = 10 + 2x$, $q_1 = 10 + 2x$, $q_1 = 2$, $q_2 = 3 + 2x$. Find the transition matrix from $B$ to $B'$.
I've seen some others answer to similar questions online, but I really have no idea why they are doing certain steps. All I understand is to write $B$ in terms of $B'$ as a linear combination like $p_1 = q_1 + q_2 \implies 6 + 3x = 2 + 3 + 2x$.
I just really have no idea how to solve this type of problem. I can do it without the values being equations but how would you do it when the values are equations?