Answer
$x=0, x\approx0.69$
Work Step by Step
Begin by factoring the terms using trial and error. Then set the terms in each set of parentheses equal to $0$ and solve for $x$ by using the natural log on both sides of each equation.
$e^{2x}-3e^{x}+2=0$
$(e^x-1)(e^x-2)=0$
$e^x-1=0, e^x-2=0$
$e^x=1, e^x=2$
$x=0, x\approx0.69$
