Simple but conceptual question

So I may just be rusty on my algebra, but I'm covering differential equations at a basic level right now and I've seen this pop up a few times and I'd love to know the proof behind why.

I'll see either $\displaystyle 10-x=e^{-kt-c1}$ become $\displaystyle x=10-Ce^{-kt}$ or say $\displaystyle y+4=e^{\frac{-x^2}{2}+C1}$ become $\displaystyle y+4=Ce^{\frac{-x^2}{2}}$

I just don't quite see how they're pulling that C down and in front of the exponential function...can anyone offer a proof or other explanation as to why? Thanks!