Solve for y (complex solution)
\left\{\begin{matrix}y=\frac{x^{2}+2x+3}{z}\text{, }&z\neq 0\\y\in \mathrm{C}\text{, }&\left(x=-\sqrt{2}i-1\text{ or }x=-1+\sqrt{2}i\right)\text{ and }z=0\end{matrix}\right.
Solve for y
y=\frac{x^{2}+2x+3}{z}
z\neq 0
Solve for x (complex solution)
x=\sqrt{yz-2}-1
x=-\sqrt{yz-2}-1
Solve for x
x=\sqrt{yz-2}-1
x=-\sqrt{yz-2}-1\text{, }\left(z<0\text{ or }y\geq \frac{2}{z}\right)\text{ and }\left(z>0\text{ or }y\leq \frac{2}{z}\right)\text{ and }z\neq 0
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yz=x^{2}+2x+3
Swap sides so that all variable terms are on the left hand side.
zy=x^{2}+2x+3
The equation is in standard form.
\frac{zy}{z}=\frac{x^{2}+2x+3}{z}
Divide both sides by z.
y=\frac{x^{2}+2x+3}{z}
Dividing by z undoes the multiplication by z.
yz=x^{2}+2x+3
Swap sides so that all variable terms are on the left hand side.
zy=x^{2}+2x+3
The equation is in standard form.
\frac{zy}{z}=\frac{x^{2}+2x+3}{z}
Divide both sides by z.
y=\frac{x^{2}+2x+3}{z}
Dividing by z undoes the multiplication by z.
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