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'to solve this' is correct and usable in written English.
You can use it when referring to a situation or problem that needs to be addressed or solved. For example, "We must find a way to solve this issue."
Exact(59)
"I'm going to solve this.
Technology will have to solve this problem.
We are going to solve this crime.
Everyone is anxious to solve this crime.
Got to solve this equation.
"Everyone has been trying to solve this.
It would take Solomon to solve this.
"We have to solve this mystery.
I'm not trying to solve this case.
I just have to solve this.
Similar(1)
Shouldn't technology be able to solve this?
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com