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The phrase "how to solve this problem" is correct and usable in written English.
You can use it when you are referring to a specific issue that needs to be resolved. For example, "I have been struggling to figure out how to solve this problem."
Exact(47)
As social scientists, we knew exactly how to solve this problem.
He knows how to solve this problem, he knows what needs to be done.
It was the British engineer Frank Whittle who worked out how to solve this problem.
Is there anyone in this planet that knows how to solve this problem?
Democrats largely agree on the broad contours of how to solve this problem.
"I don't know how to solve this problem," he said about the asthma, which he has had for eight years.
Similar(13)
There are some minor ones, there are some discussions, but nobody says, we know how to solve this refugee problem.
I don't know how to solve this vast problem [of siloed research], but I do hope that teaching dramatic writing at MIT helps in some small way.
Possibilities of how to solve this particular problem utilising other information about the mixture, e.g. bulk properties, are shown and applied to concrete AGO feedstocks with satisfactory results.
As a result, all of the players in the shipping industry are seeking for a new means on how to solve this particular problem.
We need better ideas from our presidential candidates about how to solve this enormous problem of income inequality.
More suggestions(17)
how to solve this conundrum
how to solve this hijacking
how to address this problem
how to solve this epidemic
how to solve this droop
how to solve this type
how to manage this problem
how to combat this problem
how to conquer this problem
how to handle this problem
how to fix this problem
how to investigate this problem
how to ameliorate this problem
how to reduce this problem
how to solve this sort
how to solve this challenge
how to broach this problem
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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