I finished this problem only to find that the signs have changed and I am not sure why. Can someone please let me in on the secret?

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No secret. The negative sign was factored out of the term $\displaystyle -2x-27$ and placed in front of the entire fraction in the last line.

ahhaa I actually didn't notice that negative sign at the beginning. I get it now... (a)(b)(-c) is the same at -(a)(b)(c) Thanks!