Solve for g (complex solution)
\left\{\begin{matrix}g=\frac{m}{hy}\text{, }&h\neq 0\text{ and }y\neq 0\\g\in \mathrm{C}\text{, }&m=0\text{ and }h=0\text{ and }y\neq 0\end{matrix}\right.
Solve for h (complex solution)
\left\{\begin{matrix}h=\frac{m}{gy}\text{, }&g\neq 0\text{ and }y\neq 0\\h\in \mathrm{C}\text{, }&m=0\text{ and }g=0\text{ and }y\neq 0\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=\frac{m}{hy}\text{, }&h\neq 0\text{ and }y\neq 0\\g\in \mathrm{R}\text{, }&m=0\text{ and }h=0\text{ and }y\neq 0\end{matrix}\right.
Solve for h
\left\{\begin{matrix}h=\frac{m}{gy}\text{, }&g\neq 0\text{ and }y\neq 0\\h\in \mathrm{R}\text{, }&m=0\text{ and }g=0\text{ and }y\neq 0\end{matrix}\right.
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m=ghy
Multiply both sides of the equation by y.
ghy=m
Swap sides so that all variable terms are on the left hand side.
hyg=m
The equation is in standard form.
\frac{hyg}{hy}=\frac{m}{hy}
Divide both sides by hy.
g=\frac{m}{hy}
Dividing by hy undoes the multiplication by hy.
m=ghy
Multiply both sides of the equation by y.
ghy=m
Swap sides so that all variable terms are on the left hand side.
gyh=m
The equation is in standard form.
\frac{gyh}{gy}=\frac{m}{gy}
Divide both sides by gy.
h=\frac{m}{gy}
Dividing by gy undoes the multiplication by gy.
m=ghy
Multiply both sides of the equation by y.
ghy=m
Swap sides so that all variable terms are on the left hand side.
hyg=m
The equation is in standard form.
\frac{hyg}{hy}=\frac{m}{hy}
Divide both sides by hy.
g=\frac{m}{hy}
Dividing by hy undoes the multiplication by hy.
m=ghy
Multiply both sides of the equation by y.
ghy=m
Swap sides so that all variable terms are on the left hand side.
gyh=m
The equation is in standard form.
\frac{gyh}{gy}=\frac{m}{gy}
Divide both sides by gy.
h=\frac{m}{gy}
Dividing by gy undoes the multiplication by gy.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}