\(x^2-2015x+2014=0\)
\(x^2-2014x-x+2014=0\)
\(x\left(x-2014\right)-\left(x-2014\right)=0\)
\(\left(x-2014\right)\left(x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-2014=0\\x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=2014\\x=1\end{cases}}}\)
\(x^2-2015x+2014\)\(=0\)
\(\Rightarrow x^2-x-2014x+2014\)\(=0\)
\(\Rightarrow x\left(x-1\right)-2014\left(x-1\right)\)\(=0\)
\(\Rightarrow\left(x-1\right)\left(x-2014\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\x-2014=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=2014\end{cases}}\)