hubieran desestabilizado
-they/you had destabilized
Past perfect subjunctiveellos/ellas/ustedesconjugation ofdesestabilizar.

desestabilizar

De hecho, de haberlas utilizado habrían provocado una oposición masiva y hubieran desestabilizado toda la región aún más.
In fact, had they used them they would have provoked massive opposition and would have destabilised the whole region even more.
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