Solve RGR+G-BRB=0

$$R G R + G - B R B = 0$$

Solve for G (complex solution)

$$\left\{\begin{matrix}G=\frac{RB^{2}}{R^{2}+1}\text{, }&R\neq -i\text{ and }R\neq i\\G\in \mathrm{C}\text{, }&\left(R=i\text{ or }R=-i\right)\text{ and }B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply R and R to get R^{2}.

$$R^{2}G+G-BRB=0$$

Multiply B and B to get B^{2}.

$$R^{2}G+G-B^{2}R=0$$

Add B^{2}R to both sides.

$$R^{2}G+G=0+B^{2}R$$

Anything plus zero gives itself.

$$R^{2}G+G=B^{2}R$$

Combine all terms containing G.

$$\left(R^{2}+1\right)G=B^{2}R$$

The equation is in standard form.

$$\left(R^{2}+1\right)G=RB^{2}$$

Divide both sides by R^{2}+1.

$$\frac{\left(R^{2}+1\right)G}{R^{2}+1}=\frac{RB^{2}}{R^{2}+1}$$

Dividing by R^{2}+1 undoes the multiplication by R^{2}+1.

$$G=\frac{RB^{2}}{R^{2}+1}$$

Solve for G

$$G=\frac{RB^{2}}{R^{2}+1}$$

Steps for Solving Linear Equation

Multiply R and R to get R^{2}.

$$R^{2}G+G-BRB=0$$

Multiply B and B to get B^{2}.

$$R^{2}G+G-B^{2}R=0$$

Add B^{2}R to both sides.

$$R^{2}G+G=0+B^{2}R$$

Anything plus zero gives itself.

$$R^{2}G+G=B^{2}R$$

Combine all terms containing G.

$$\left(R^{2}+1\right)G=B^{2}R$$

The equation is in standard form.

$$\left(R^{2}+1\right)G=RB^{2}$$

Divide both sides by R^{2}+1.

$$\frac{\left(R^{2}+1\right)G}{R^{2}+1}=\frac{RB^{2}}{R^{2}+1}$$

Dividing by R^{2}+1 undoes the multiplication by R^{2}+1.

$$G=\frac{RB^{2}}{R^{2}+1}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\sqrt{GR+\frac{G}{R}}\text{; }B=\sqrt{GR+\frac{G}{R}}\text{, }&R\neq 0\\B\in \mathrm{C}\text{, }&G=0\text{ and }R=0\end{matrix}\right.$$

Solve for B

$$\left\{\begin{matrix}B=\sqrt{GR+\frac{G}{R}}\text{; }B=-\sqrt{GR+\frac{G}{R}}\text{, }&\left(G\geq 0\text{ and }R>0\right)\text{ or }\left(G\leq 0\text{ and }R<0\right)\\B\in \mathrm{R}\text{, }&G=0\text{ and }R=0\end{matrix}\right.$$