Question: Cambridge Dictionary gives this definition about "complain"

> 
> to say that something is wrong or not satisfactory
> 
> 
> 

and this definition about "complaint"

> 
> a statement that something is wrong or not satisfactory
> 
> 
> 

I guess both of them means the same thing. However, [Google Ngram](https://books.google.com/ngrams/graph?content=to%20complain%20about%2C%20make%20a%20complaint%20about%20&case_insensitive=on&year_start=1800&year_end=2008&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cto%20complain%20about%3B%2Cc0%3B.t1%3B%2Cmake%20a%20complaint%20about%3B%2Cc0#t1%3B%2Cto%20complain%20about%3B%2Cc0%3B.t1%3B%2Cmake%20a%20complaint%20about%3B%2Cc0) shows that the former is much more commonly used that the latter

[![enter image description here](https://i.stack.imgur.com/IyIrh.png)](https://i.stack.imgur.com/IyIrh.png)

Are those two expressions interchangeable?

Answer: 
No. No, no, no. Send your friends back a grade.

*Conclusion* is singular. Use *is*.

*Both* is plural. Use *are*.
No reason they can't be used in the same sentence, but for the sentence you provided it's incorrect.

The context of the question is "can you use both or only one", so "both" is *a solution* and therefore:

"The conclusion is [the use of] both is harmful."

In the original sentence, "The conclusion is both are harmful.", this is implying that *both* words "is" and "are" are independently harmful, and they are not both harmful.