The phrase "with both eyes closed" is an idiom that means doing something easily or without effort. It can also mean being blinded by bias or ignorance. Some synonyms for this phrase include "without thinking twice," "effortlessly," "blindly," "automatically," "unquestioningly," "unhesitatingly," and "confidently." These words can be used to convey the same meaning as "with both eyes closed" in different contexts. When writing an essay or a speech, using synonyms can add variety to the language and make the message more engaging for the audience.