Make This Solvable

Given that $ab+ac=abc \iff a(b+c)=a(bc)$

Now we need to remove $a$ on both sides. Unfortunately, no variable has provided condition, while to eliminate $a$ , we need $a \neq 0$ so that the equation above solvable.

given $a\neq 0$

$a(b+c)=abc \implies b+c=bc \implies b(1-c)=-c$

since $c$ and $1-c$ are relatively primes, $1-c= -1 \implies c=2 \implies b=2$

So, given $a$ can be eliminated, $b,c$ can be determined uniquely. Therefore, $a$ should be given.

Thank youo veri mucho!