Solve x^mx^2m=2

$$x ^ { m } x ^ { 2 m } = 2$$

Solve for m (complex solution)

$$m=\frac{2\pi n_{1}i}{3\ln(x)}+\frac{\log_{x}\left(2\right)}{3}$$

$$n_{1}\in \mathrm{Z}$$

$$x\neq 1\text{ and }x\neq 0$$

Solve for x (complex solution)

$$x=e^{-\frac{2\pi n_{1}\left(Im(m)+iRe(m)\right)}{3\left(\left(Re(m)\right)^{2}+\left(Im(m)\right)^{2}\right)}}\times 2^{\frac{Re(m)-iIm(m)}{3\left(\left(Re(m)\right)^{2}+\left(Im(m)\right)^{2}\right)}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for m

$$m=\frac{\log_{x}\left(2\right)}{3}$$

$$x\neq 1\text{ and }x>0$$

Solve for x

$$\left\{\begin{matrix}x=-2^{\frac{1}{3m}}\text{, }&m\neq 0\text{ and }Numerator(m)\text{bmod}2=0\text{ and }Denominator(m)\text{bmod}2=1\\x=2^{\frac{1}{3m}}\text{, }&m\neq 0\end{matrix}\right.$$