2bc+bd-b+3=-4c-4 solve for b.
My answer was: b=(-4c-7)/2c+d-1
The answer should have been: b=(4c+7)/-2c+d-1
I know that they multiplied by -1 to get the proper answer, but I really just don't understand WHY?

Actually, they didn't multiply by -1 to get the proper answer and your answer is fine like it is. It's just that the other is a little more... 'elegant' one might say. They actually multiplied by 1.

\frac{-4c-7}{2c+d-1} \times \frac{-1}{-1}= \frac{4c+7}{-2c-d+1}

Remember that -1/-1 = 1