Complex sentence: Having managed to quietly depose their father, the brothers now had to deal with Constantine VII. Unfortunately for them, rumours soon spread around Constantinople, to the effect that, following Romanos's deposition, Constantine VII's life was in danger.
Split into simpler sentences: Having managed to quietly depose their father, the brothers now had to deal with Constantine VII. Unfortunately for them, their actions were no longer secret. Rumours of the deposition soon spread around Constantinople, to the effect that Constantine VII's life was in danger.