Find the largest value of $c$ such that $\frac{c^2 + 6c -27}{c-3} +2c = 23$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the largest value of $c$ such that $\frac{c^2 + 6c -27}{c-3} +2c = 23$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{14}{3}
Find the largest value of $c$ such that $\frac{c^2 + 6c -27}{c-3} +2c = 23$.
train