## Elementary Technical Mathematics

$$v_0= 2 v-v_f .$$
We have: $$v=\frac{v_f+v_0}{2}$$ We multiply both sides by $2$ and then group the like terms: $$2v=\frac{v_f+v_0}{2}2\Longrightarrow2 v=v_f+v_0\Longrightarrow v_0= 2 v-v_f .$$