Usually one attempts to talk oneself out of the blame of a "case" etc. To "bortforklare" is to explain so that things probably aren't by far as clear later. Not an honest way of explaining, in other words.

Could also use "try to explain" - as opposed to "really explain".

"Han forsøkte å bortforklare den høye prisen ved å si at den internasjonale kursen på kroner var dårlig."

"He tried to explain the higher prices by saying the exchange rate for kroner was bad."

.....according to my knowledge/blåordbok - however it depends on your context. You might also use
Rationalise
Validate
It depends on what the context is Erling.
HTH
Andy Bell

I also like 'talk oneself out of', while 'explain away' somehow misses the mark. The full meaning of bortforklare would be something like 'present your case in such a manner that no blame is attached to yourself or your cause'. Some actions cannot be justified, while they might be explainable - although 'explain away' is moot where blame is concerned. The medical angle - explaining away symptoms to alleviate patient concerns - is a completely inappropriate translation for bortforklare, which always assumes a wrong has been committed and needs to be explained, excused or justified. There is also very little actual explanation involved in 'bortforklare' -it's more a statement of 'why wasn't it wrong for me to do it' than 'why did I do it'.

sounds smoother to me.