Solve for A_0 (complex solution)
\left\{\begin{matrix}A_{0}=\frac{\left(x+1\right)\left(x+2\right)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\A_{0}\in \mathrm{C}\text{, }&\left(x=-1\text{ or }x=-2\right)\text{ and }f=0\end{matrix}\right.
Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{\left(x+1\right)\left(x+2\right)}{A_{0}x}\text{, }&x\neq 0\text{ and }A_{0}\neq 0\\f\in \mathrm{C}\text{, }&\left(x=-1\text{ or }x=-2\right)\text{ and }A_{0}=0\end{matrix}\right.
Solve for A_0
\left\{\begin{matrix}A_{0}=\frac{\left(x+1\right)\left(x+2\right)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\A_{0}\in \mathrm{R}\text{, }&\left(x=-1\text{ or }x=-2\right)\text{ and }f=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{\left(x+1\right)\left(x+2\right)}{A_{0}x}\text{, }&x\neq 0\text{ and }A_{0}\neq 0\\f\in \mathrm{R}\text{, }&\left(x=-1\text{ or }x=-2\right)\text{ and }A_{0}=0\end{matrix}\right.
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fxA_{0}=x^{2}+3x+2
The equation is in standard form.
\frac{fxA_{0}}{fx}=\frac{\left(x+1\right)\left(x+2\right)}{fx}
Divide both sides by fx.
A_{0}=\frac{\left(x+1\right)\left(x+2\right)}{fx}
Dividing by fx undoes the multiplication by fx.
A_{0}xf=x^{2}+3x+2
The equation is in standard form.
\frac{A_{0}xf}{A_{0}x}=\frac{\left(x+1\right)\left(x+2\right)}{A_{0}x}
Divide both sides by A_{0}x.
f=\frac{\left(x+1\right)\left(x+2\right)}{A_{0}x}
Dividing by A_{0}x undoes the multiplication by A_{0}x.
fxA_{0}=x^{2}+3x+2
The equation is in standard form.
\frac{fxA_{0}}{fx}=\frac{\left(x+1\right)\left(x+2\right)}{fx}
Divide both sides by fx.
A_{0}=\frac{\left(x+1\right)\left(x+2\right)}{fx}
Dividing by fx undoes the multiplication by fx.
A_{0}xf=x^{2}+3x+2
The equation is in standard form.
\frac{A_{0}xf}{A_{0}x}=\frac{\left(x+1\right)\left(x+2\right)}{A_{0}x}
Divide both sides by A_{0}x.
f=\frac{\left(x+1\right)\left(x+2\right)}{A_{0}x}
Dividing by A_{0}x undoes the multiplication by A_{0}x.
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