I am trying to draw x=3e^4t+12e^-t where t is x axis and x is y axis

I don't understand how from visualising this i can tell it is a growing function and doesntcross the t axis. I drew for instance y = -2e^4t +12e^-t since I knew it would cross the t axis as I could put y=0 and solve it.

Putting x=o however apparantly cannot be solved. Where am I going wrong,

0 = 3e^4t + 12e^-t

-e^4t = 4e^-t

e^4t = -4e^-t

lne^4t = -ln4 + lne^-t

4t = -ln4 -t

t = -(ln4)/5