Solve for M (complex solution)
M=\sqrt{\frac{k\left(4y-k+2\right)}{2y+1}}
y\neq -\frac{1}{2}
Solve for k (complex solution)
k=-\sqrt{\left(2y+1\right)\left(2y-M^{2}+1\right)}+2y+1
k=\sqrt{\left(2y+1\right)\left(2y-M^{2}+1\right)}+2y+1\text{, }y\neq -\frac{1}{2}\text{ and }\left(M=0\text{ or }arg(M)<\pi \right)
Solve for M
M=\sqrt{\frac{k\left(4y-k+2\right)}{2y+1}}
\left(k\geq 0\text{ and }k\leq 4y+2\text{ and }y\neq -\frac{1}{2}\right)\text{ or }\left(k\geq 0\text{ and }y<-\frac{1}{2}\right)\text{ or }\left(k\leq 4y+2\text{ and }y<-\frac{1}{2}\right)
Solve for k
k=-\sqrt{-\left(2y+1\right)\left(-2y+M^{2}-1\right)}+2y+1
k=\sqrt{-\left(2y+1\right)\left(-2y+M^{2}-1\right)}+2y+1\text{, }\left(M\leq \sqrt{2y+1}\text{ or }y<-\frac{1}{2}\right)\text{ and }M\geq 0\text{ and }y\neq -\frac{1}{2}
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