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"reached by both" is correct and usable in written English
You can use it when two different parties have achieved the same result or outcome. For example, "The decision was finally reached by both the parties after long negotiations."
Exact(21)
That conclusion, reached by both men before Ireland's Nice vote, seems even more relevant now.
Clausen said he has nothing to refute the conclusion, reached by both [Ron Hamilton] and Krakauer, that ODAP was present.
"Over the years, judicial and law enforcement departments of China and the US have taken positive steps to implement the political consensus reached by both governments, and work in unison to fight against transnational corruption crimes," Mr Zhu said.
(It might have been argued that after a certain level of destructive capability had been reached by both sides, an effective stalemate would be reached and extra weapons would make little difference, promising only, as British Prime Minister Winston Churchill put it, to make "the rubble bounce").
This was a critical moment in the loss and damage genealogy as it was a compromise reached by both developed and developing countries to move this discussion forward.
The maximum achievable sum rate is about 51 bits per channel use, reached by both the centralized and graph-based techniques.
Similar(39)
Reached by telephone, both Ms. Gould and Mr. Stein said their departures were predicated partly on Mr. Sicha leaving.
"There is profitability to be reached by combining both video and music together," and attracting more subscribers that way, Larner says.
Under the optimal conditions, 100% decoloration of dye solution can be reached by using both processes, but with different accumulated solar energy (SPF system: 34 W h, SPFox system: 16 W h).
Under the optimal conditions, 100% decoloration of dye solution can be reached by using both processes (SPFox with H2O2 addition at the beginning or along the reaction) but with different reaction rates.
A total score is reached by combining both subscales.
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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