Answer
$x=\frac{1}{2}$
Work Step by Step
Factor the left side of the equation to get $e^{x}(1-2x)=0$. If one of the factors equal zero, the entire expression equals zero. $e^{x}$ can never equal zero, so there is no solution. Solving $1-2x=0$ by adding $2x$ to each side and dividing by $2$ leaves $x=\frac{1}{2}$.
