Find the bifurcations (if any) and their type:

$\displaystyle x'=x^3-sinh(x+ \mu^3)$

So if we call that function f, I need f = f' = 0 right?

Well that gives me

$\displaystyle x^3-sinh(x+\mu^3)=3x^2-cosh(x+\mu^3)=0$

Some simple manipulation gives:

$\displaystyle cosh(x+\mu^3)^3-27cosh(x+\mu^3)^2+27=0$

What am I doing wrong? I cannot solve this.