Solve 5nA=G-BA

$$5 n A = G - B A$$

Solve for A

$$\left\{\begin{matrix}A=\frac{G}{5n+B}\text{, }&n\neq -\frac{B}{5}\\A\in \mathrm{R}\text{, }&G=0\text{ and }n=-\frac{B}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add BA to both sides.

$$5nA+BA=G$$

Combine all terms containing A.

$$\left(5n+B\right)A=G$$

Divide both sides by 5n+B.

$$\frac{\left(5n+B\right)A}{5n+B}=\frac{G}{5n+B}$$

Dividing by 5n+B undoes the multiplication by 5n+B.

$$A=\frac{G}{5n+B}$$

Solve for B

$$\left\{\begin{matrix}B=-5n+\frac{G}{A}\text{, }&A\neq 0\\B\in \mathrm{R}\text{, }&G=0\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$G-BA=5nA$$

Subtract G from both sides.

$$-BA=5nA-G$$

The equation is in standard form.

$$\left(-A\right)B=5An-G$$

Divide both sides by -A.

$$\frac{\left(-A\right)B}{-A}=\frac{5An-G}{-A}$$

Dividing by -A undoes the multiplication by -A.

$$B=\frac{5An-G}{-A}$$

Divide 5nA-G by -A.

$$B=-5n+\frac{G}{A}$$