Does one say
Plugging in that value into the previous equation...
Plugging that value in the previous equation...
or something else?
A combination of your two examples would be correct:
Plugging that value into the previous equation..
In this sentence you are dealing with the phrasal verb 'plug in', which has then been split by the noun ('that value').
Either "Plug in that value" or "plug that value into" are fine depending on the rest of the sentence, but not "Plug in that value into".
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