Find the value of $n$ that satisfies $2(n+1)!+6n!=3(n+1)!$, where $n! = n\cdot (n-1)\cdot (n-2) \cdots 2\cdot 1$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the value of $n$ that satisfies $2(n+1)!+6n!=3(n+1)!$, where $n! = n\cdot (n-1)\cdot (n-2) \cdots 2\cdot 1$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5
Find the value of $n$ that satisfies $2(n+1)!+6n!=3(n+1)!$, where $n! = n\cdot (n-1)\cdot (n-2) \cdots 2\cdot 1$.
train