迎yíng刃rèn而ér解jiě

Literal: meet the blade and split apart
Figurative: Of a problem: to sort itself out easily, almost on its own, once the key point is tackled; it usually follows a condition (只要…就…).

Where does 迎刃而解 come from?

It comes from the same speech by General Du Yu that gave us 势如破竹, recorded in his biography in the 《晋书》: the army, he said, was already like bamboo being split, since once past the first joints the rest of the stalk falls open at the touch of the blade. 迎 means "to meet," 刃 "the edge," and 解 "to come apart." From that image the idiom kept an idea different from 势如破竹: not unstoppable momentum, but that once the hard part is done, the rest gives way without effort. Today it is used for problems and doubts, usually after the step that unlocks them: "do this, and the rest will sort itself out."

Source (出处): 《晋书·杜预传》

How is 迎刃而解 used? Two examples

只zhǐ要yào把bǎ基jī础chǔ语yǔ法fǎ搞gǎo懂dǒng，后hòu面miàn的de难nán题tí就jiù迎yíng刃rèn而ér解jiě了le。
Once you get the basic grammar down, the harder problems further on will solve themselves.
找zhǎo到dào漏lòu水shuǐ的de那nà根gēn管guǎn子zi以yǐ后hòu，楼lóu下xià的de麻má烦fan也yě迎yíng刃rèn而ér解jiě了le。
Once we found the leaking pipe, the trouble with the downstairs neighbors cleared up on its own.

In Wanyu, all 400 chengyu have audio on every sentence, and you can save them to your decks and review them with spaced repetition. Free.