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The phrase "a problem that is both" is correct and usable in written English.
You can use it when discussing a problem that has two characteristics or aspects simultaneously.
Example: "We are facing a problem that is both complex and urgent, requiring immediate attention."
Alternatives: "a challenge that is both" or "an issue that is both".
Exact(7)
A problem that is both NP and NP-hard is said to be NP-complete.
The N.C.A.A. has a problem that is both optical and practical, and it's becoming impossible to ignore.
(Not all NP-hard problems are members of the class of NP problems, however). A problem that is both NP and NP-hard is said to be NP-complete.
This provides a measure of hope for a problem that is both heartbreaking and growing.
Proponents of such measures say that they help combat voter fraud, a problem that is both rare and largely not possible to prevent with voter ID laws.
While at first glance, it is easy to dismiss people who hoard as lazy or simply messy, such characterizations don't do justice to a problem that is both layered and complex.
Similar(53)
Stroke is a global health-care problem that is both serious and disabling [ 1].
Please take note, however, that this is only one perspective on a problem that is the subject of fierce debate both inside and outside the medical profession.
It was a problem that was disturbing both the Charity Commission and the National Council for Voluntary Organisations (NCVO), the umbrella group for national charities.
This is going to be a trend in the future, it's part of the discussions we're having -- I'm -- I'm in the midst of having some discussions in the private sector with -- this is going to be a problem that's common to both of us.
Still, it's a problem that's important to both of them and the rest of the people that worked on it.
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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