Prove that language is regular given other regular language

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Let $L\subseteq A^*$ be regular. Prove that $L'$ is regular where $L' = \{vw \mid \exists u\in A^*\ vuw \in L\wedge |u|=|w|+|v|\}$

Help me please. It is very hard for me, I don't know how to start. This type of exercises is extremely hard.