This is a problem I came across in my Calculus textbook: g(x)=e^(-x)+e^(3x)

I am asked to find the open intervals over which this function increases and decreases. The original function isn't undefined for any value of x so I proceeded to find the derivative: g'(x)=3e^(3x)-e^(-x)

For the critical numbers there are no values of x for which this function is undefined (where the original is defined) but there seems to be one value of x for which the derivative will be equal to zero.

This is an odd-numbered problem in the book, so I checked the website to see what the critical number would be. The website stated that g'(x)=3e^(3x)-e^(-x)=0

when x=-(1/4)ln(3).

However the website did not show the steps to arrive at such a result. Would anyone be so kind as to explain the steps it takes to arrive at this possible critical number?

This website: http://www.calcchat.com/book/Calculus-ETF-5e/ and the input section 4.3 # 17 is the problem I am dealing with.