e4x-13e2x+12=0
$$e^{4x}-13e^{2x}+12=0$$
This can be written as:
$$(e^{2x})^2-13e^{2x}+12=0$$
which can be written in turn as:
$$(e^{2x}-1)(e^{2x}-12)=0$$
So we have:
1.
$$\\e^{2x}=1\\so\\x=0$$
2.
$$\\e^{2x}=12\\\\2x=\ln{12}\\\\x=\frac{\ln{12}}{2}$$
.