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?

Note that the entire equation is of the form
$$
a^3 + b^3 = (a+b)^3
$$
with $a = 2\cdot 3^x$ and $b = 9^x - 3$. This reduces to
$$
0 = 3a^2b + 3ab^2\\
0 = 3ab(a+b)
$$
which has the three solutions $a = 0$, $b = 0$, or $a+b = 0$. Clearly, $a = 0$ can't happen. $b = 0$ means $9^x = 3$, which has the solution $x = \frac12$. Finally, $a+b = 0$ means
$$
2\cdot 3^x + 9^x - 3 = 0\\
(3^x)^2 + 2\cdot 3^x - 3 = 0\\
3^x = \frac{-2\pm\sqrt{2^2 - 4\cdot 1\cdot (-3)}}{2} = -1\pm 2
$$
Since $3^x$ can't be negative, we can only keep $3^x = 1$, which gives $x = 0$.
