Solve for H (complex solution)
\left\{\begin{matrix}H=\frac{kx^{2}}{2gm}\text{, }&g\neq 0\text{ and }m\neq 0\\H\in \mathrm{C}\text{, }&\left(k=0\text{ and }g=0\right)\text{ or }\left(x=0\text{ and }g=0\right)\text{ or }\left(x=0\text{ and }m=0\text{ and }g\neq 0\right)\text{ or }\left(k=0\text{ and }m=0\text{ and }g\neq 0\right)\end{matrix}\right.
Solve for g (complex solution)
\left\{\begin{matrix}g=\frac{kx^{2}}{2Hm}\text{, }&H\neq 0\text{ and }m\neq 0\\g\in \mathrm{C}\text{, }&\left(k=0\text{ and }H=0\right)\text{ or }\left(x=0\text{ and }H=0\right)\text{ or }\left(x=0\text{ and }m=0\text{ and }H\neq 0\right)\text{ or }\left(k=0\text{ and }m=0\text{ and }H\neq 0\right)\end{matrix}\right.
Solve for H
\left\{\begin{matrix}H=\frac{kx^{2}}{2gm}\text{, }&g\neq 0\text{ and }m\neq 0\\H\in \mathrm{R}\text{, }&\left(k=0\text{ and }g=0\right)\text{ or }\left(x=0\text{ and }g=0\right)\text{ or }\left(x=0\text{ and }m=0\text{ and }g\neq 0\right)\text{ or }\left(k=0\text{ and }m=0\text{ and }g\neq 0\right)\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=\frac{kx^{2}}{2Hm}\text{, }&H\neq 0\text{ and }m\neq 0\\g\in \mathrm{R}\text{, }&\left(k=0\text{ and }H=0\right)\text{ or }\left(x=0\text{ and }H=0\right)\text{ or }\left(x=0\text{ and }m=0\text{ and }H\neq 0\right)\text{ or }\left(k=0\text{ and }m=0\text{ and }H\neq 0\right)\end{matrix}\right.
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kx^{2}=2mgH
Multiply both sides of the equation by 2.
2mgH=kx^{2}
Swap sides so that all variable terms are on the left hand side.
2gmH=kx^{2}
The equation is in standard form.
\frac{2gmH}{2gm}=\frac{kx^{2}}{2gm}
Divide both sides by 2mg.
H=\frac{kx^{2}}{2gm}
Dividing by 2mg undoes the multiplication by 2mg.
kx^{2}=2mgH
Multiply both sides of the equation by 2.
2mgH=kx^{2}
Swap sides so that all variable terms are on the left hand side.
2Hmg=kx^{2}
The equation is in standard form.
\frac{2Hmg}{2Hm}=\frac{kx^{2}}{2Hm}
Divide both sides by 2mH.
g=\frac{kx^{2}}{2Hm}
Dividing by 2mH undoes the multiplication by 2mH.
kx^{2}=2mgH
Multiply both sides of the equation by 2.
2mgH=kx^{2}
Swap sides so that all variable terms are on the left hand side.
2gmH=kx^{2}
The equation is in standard form.
\frac{2gmH}{2gm}=\frac{kx^{2}}{2gm}
Divide both sides by 2mg.
H=\frac{kx^{2}}{2gm}
Dividing by 2mg undoes the multiplication by 2mg.
kx^{2}=2mgH
Multiply both sides of the equation by 2.
2mgH=kx^{2}
Swap sides so that all variable terms are on the left hand side.
2Hmg=kx^{2}
The equation is in standard form.
\frac{2Hmg}{2Hm}=\frac{kx^{2}}{2Hm}
Divide both sides by 2mH.
g=\frac{kx^{2}}{2Hm}
Dividing by 2mH undoes the multiplication by 2mH.
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Limits
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