。
You can solve that problem without being violent.
Literal
Violent [attributive-な] thing [object-を] do-not-even, that [attributive-の] problem [topic-は] solve-can.
~なくても ('even without doing X / even if X isn't done') is the concessive negative — a combination of ~ない + ても. 解決する is a suru-verb for 'to solve / resolve.' できる is the plain potential of する. Learners should note the subtle parse: 乱暴なこと as one noun phrase ('violent things') then ~をしなくても.