Find the constant $c$ such that $$(x^2-4x+3)(x+5) - (x^2+4x-5)(x-c)=0$$ for all $x.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the constant $c$ such that $$(x^2-4x+3)(x+5) - (x^2+4x-5)(x-c)=0$$ for all $x.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
Find the constant $c$ such that $$(x^2-4x+3)(x+5) - (x^2+4x-5)(x-c)=0$$ for all $x.$
train