I found the sentence
And I have a doubt about using of 置く置かない How should it be translated ? and How to use it I have never seen this grammar using before
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「Verb in Affirmative Form + Same Verb in Negative Form」
is a common expression meaning:
"(a discussion of) the pros and cons of [Verb]-ing" or
"whether or not one should [Verb]"
Thus, the passage:
"My wife left home after the fight. The cause of our fight was regarding whether or not we should take in boarders/lodgers at our home."