Cubed exponent equation 
$$\left(2 · 3^x\right)^3 + \left(9^x − 3\right)^3 = \left(9^x + 2 · 3^x − 3\right)^3$$ Solve the equation

I got the answer to the problem, in which I evaluated the whole expression (which was quite hard) which was $0$ and $1/2$, is there a way to solve this problem in a less tedious way?

Using $t:=3^x$ and following the factorization by @Arthur ($(a+b)^3-a^3-b^3=3ab(a+b)$), the equation is equivalent to
$$t(t^2-3)(t^2+2t-3)=t(t-\sqrt 3)(t+\sqrt 3)(t-1)(t+3)=0.$$
Only the positive $t$ yield a solution and we immediately have
$$x=\frac12\text{ or }x=0.$$
