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The phrase "adapted by both" is correct and usable in written English.
It can be used when referring to something that has been modified or changed by two parties or entities.
Example: "The script was adapted by both the director and the screenwriter to better fit the vision of the film."
Alternatives: "modified by both" or "altered by both".
Exact(2)
Brennan said leaders needed to formalise "Indigenous aspiration" into a program that could be accepted or adapted by both Abbott and opposition leader Bill Shorten (or their successors) in the next parliament.
It was taken over and adapted by both Plato and Aristotle and remained the dominant theory throughout antiquity (Barker 1989, 41 n. 47).
Similar(57)
A third test, the function-aided sum test, was adapted by incorporating both biological function prediction (Ramensky et al. 2002) and allele frequency into the weighting process (Price et al. 2010).
Adapted by Patrick Barlow from both the classic spy movie and the John Buchan novel of 1915, this fast, frothy exercise in legerdemain is throwaway theater at its finest.
Two new adaptations of Ibsen and Strindberg classics -- both awash in marital woe and both adapted by bright American talents -- are wheeling into sight for possible spring productions.
In Designing the New American University, Crow and coauthor William B. Dabars a historian whose research focus is the American research university examine the emergence of this set of institutions and the imperative for the new model, the tenets of which may be adapted by colleges and universities, both public and private.
As to c1 and c2, both are adapted by the same equation.
Perhaps one or both of those stories will be adapted by the BBC at some point.
Adapted by Sharon Arms Doucet.
Adapted by George Bartenieff and Karen Malpede.
Adapted by David Hare.
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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