Search and Replace Trailing Space in Libreoffice

Edit > Find & Replace

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Search for: ^[ ]+|[ ]+$
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Replace with:
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Options: Regular expressions: ON
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Click "Replace All".

In English, that pattern matches:

1
Beginning of text
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A space, zero or more times
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(Any character, zero or more times)
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A space, zero or more times
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End of text

The replacement represents the text that matched the part in parentheses, or everything except the spaces at the end.