proving a statement with multiple quantifiers

Question

F is just a field, and a,b,c are members. There are 3 quantifiers, which is a bit confusing for me, so I'm not sure where to start exactly. I get that C should be "universal", but then I get stuck. $$ \forall a\in \mathbb F \quad \exists b\in \mathbb F \quad \forall c \in \mathbb F \quad c+b=1_\mathbb F\quad \Longrightarrow \quad a(ac+1)=0_\mathbb F $$