Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{y}{2x}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y}{2f}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }f=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{y}{2x}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y}{2f}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }f=0\end{matrix}\right.
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2fx=y
Swap sides so that all variable terms are on the left hand side.
2xf=y
The equation is in standard form.
\frac{2xf}{2x}=\frac{y}{2x}
Divide both sides by 2x.
f=\frac{y}{2x}
Dividing by 2x undoes the multiplication by 2x.
2fx=y
Swap sides so that all variable terms are on the left hand side.
\frac{2fx}{2f}=\frac{y}{2f}
Divide both sides by 2f.
x=\frac{y}{2f}
Dividing by 2f undoes the multiplication by 2f.
2fx=y
Swap sides so that all variable terms are on the left hand side.
2xf=y
The equation is in standard form.
\frac{2xf}{2x}=\frac{y}{2x}
Divide both sides by 2x.
f=\frac{y}{2x}
Dividing by 2x undoes the multiplication by 2x.
2fx=y
Swap sides so that all variable terms are on the left hand side.
\frac{2fx}{2f}=\frac{y}{2f}
Divide both sides by 2f.
x=\frac{y}{2f}
Dividing by 2f undoes the multiplication by 2f.
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
699 * 533
Matrix
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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}