Math Help - Simplification problem

1. Simplification problem

My brain is frying, for some reason.

For the equation:

$

B=(1-a)c+aB

$

...I understand that this simplifies to $B=c$, but for some reason, I can't figure out why. Can someone help to refresh and embarass me?

2. Subtract $aB$ from both sides

$B-aB = (1-a)c$

Factor the LHS and see what cancels

Bear in mind that $a \neq 1$

3. Yup, my brain was fried. Thanks for pointing out what I wasn't seeing.