If $c | b(x, y, z,...)$, does $c | b$?

Question

If $c$ divides something like $bxcd + bhdwou + bn$, does $ c | b$?

I'm confused because say that's true. Then let $c = 5$ and $b = 6$.

Then $c | b(10)$, but $5$ does not divide $6$.

So it this false?

If it is false, how come the solution to this, $c|abx + cby$ is true in my textbook?

edit: My bad, I was missing some info from the question, I'll delete soon

Answer 1

Hint: Let $p\in\Bbb N$. Then $p$ is prime if and only if for all $a,b\in\Bbb N$, whenever $p\mid ab$, we have either $p\mid a$ or $p\mid b$.

Answer 2

If $(xcd + hdwou + n,c)=1$,it's true.

More precisely, if $a|bc$ and $(a,c)=1$,then $a|b $.

I can't comment about the textbook problem, as context is missing.