Solve for r (complex solution)
\left\{\begin{matrix}r=-\frac{st}{uv}\text{, }&u\neq 0\text{ and }v\neq 0\\r\in \mathrm{C}\text{, }&\left(t=0\text{ and }v=0\right)\text{ or }\left(t=0\text{ and }u=0\right)\text{ or }\left(s=0\text{ and }v=0\right)\text{ or }\left(s=0\text{ and }u=0\right)\end{matrix}\right.
Solve for s (complex solution)
\left\{\begin{matrix}s=-\frac{ruv}{t}\text{, }&t\neq 0\\s\in \mathrm{C}\text{, }&\left(r=0\text{ or }v=0\text{ or }u=0\right)\text{ and }t=0\end{matrix}\right.
Solve for r
\left\{\begin{matrix}r=-\frac{st}{uv}\text{, }&u\neq 0\text{ and }v\neq 0\\r\in \mathrm{R}\text{, }&\left(t=0\text{ and }v=0\right)\text{ or }\left(t=0\text{ and }u=0\right)\text{ or }\left(s=0\text{ and }v=0\right)\text{ or }\left(s=0\text{ and }u=0\right)\end{matrix}\right.
Solve for s
\left\{\begin{matrix}s=-\frac{ruv}{t}\text{, }&t\neq 0\\s\in \mathrm{R}\text{, }&\left(r=0\text{ or }v=0\text{ or }u=0\right)\text{ and }t=0\end{matrix}\right.
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\left(-r\right)vu=ts
Swap sides so that all variable terms are on the left hand side.
-ruv=st
Reorder the terms.
\left(-uv\right)r=st
The equation is in standard form.
\frac{\left(-uv\right)r}{-uv}=\frac{st}{-uv}
Divide both sides by -uv.
r=\frac{st}{-uv}
Dividing by -uv undoes the multiplication by -uv.
r=-\frac{st}{uv}
Divide ts by -uv.
st=-ruv
Reorder the terms.
ts=-ruv
The equation is in standard form.
\frac{ts}{t}=-\frac{ruv}{t}
Divide both sides by t.
s=-\frac{ruv}{t}
Dividing by t undoes the multiplication by t.
\left(-r\right)vu=ts
Swap sides so that all variable terms are on the left hand side.
-ruv=st
Reorder the terms.
\left(-uv\right)r=st
The equation is in standard form.
\frac{\left(-uv\right)r}{-uv}=\frac{st}{-uv}
Divide both sides by -uv.
r=\frac{st}{-uv}
Dividing by -uv undoes the multiplication by -uv.
r=-\frac{st}{uv}
Divide ts by -uv.
st=-ruv
Reorder the terms.
ts=-ruv
The equation is in standard form.
\frac{ts}{t}=-\frac{ruv}{t}
Divide both sides by t.
s=-\frac{ruv}{t}
Dividing by t undoes the multiplication by t.
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