yogi_Extract Data Between Two Specified Characters With The Character Appearing At Different Places In A String

Yogi Anand, D.Eng, P.E.                                         Google Spreadsheet                            www.energyefficientbuild.com

Lit said:
How do I extract specifc data between two ' apostrophes when there are four apostrophes at different places in the cell?
My data has the following text in cell column A, cells 2 through 600.
xxxxxxxxxx['K0143M678Z'] = '0';
I need to only pull out the data starting after the first apostrophe which is after the first "[" (box bracket).
The data after the apostrophe changes i.e., it may become '1x34xs24xx' and won't always be "K" but it will more than likely stay limited to 10 characters
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In the following I present my convoluted solution for a generalized case in regard to the character used and the starting and ending position of the character.