\(2x.3^x=3^x+2x+1\)
\(\Rightarrow2x.3^x-3^x-2x-1=0\)
\(\Rightarrow3^x.\left(2x+1\right)-\left(2x+1\right)=0\)
\(\Rightarrow\left(3^x-1\right)\left(2x+1\right)=0\)
\(\Rightarrow3^x-1=0\) hoặc \(2x+1=0\)
\(\Rightarrow3^x=1\) hoặc \(2x=-1\)
\(\Rightarrow x\in\left\{-\frac{1}{2};0\right\}\)