Let \(f:R\to R\) be defined as \(f\left(x\right)=a{e}^{2x}+b{e}^{x}+cx.\) If \(f\left(0\right)=-1,f'\left({\log }_{e}2\r…

Let \(f:R\to R\) be defined as

\(f\left(x\right)=a{e}^{2x}+b{e}^{x}+cx.\)

If \(f\left(0\right)=-1,f'\left({\log }_{e}2\right)=21\) and

\({\int }_{0}^{{\log }_{e}4}\left(f\left(x\right)-cx\right)dx=\frac{39}{2},\) then the

value of \(\left|a+b+c\right|\) equals