Solve A*B^2=(A-3)(2B)

$$A \times B ^ { 2 } = ( A - 3 ) ( 2 B )$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{6}{B-2}\text{, }&B\neq 2\\A\in \mathrm{R}\text{, }&B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply A-3 by 2.

$$AB^{2}=\left(2A-6\right)B$$

Use the distributive property to multiply 2A-6 by B.

$$AB^{2}=2AB-6B$$

Subtract 2AB from both sides.

$$AB^{2}-2AB=-6B$$

Combine all terms containing A.

$$\left(B^{2}-2B\right)A=-6B$$

Divide both sides by B^{2}-2B.

$$\frac{\left(B^{2}-2B\right)A}{B^{2}-2B}=-\frac{6B}{B^{2}-2B}$$

Dividing by B^{2}-2B undoes the multiplication by B^{2}-2B.

$$A=-\frac{6B}{B^{2}-2B}$$

Divide -6B by B^{2}-2B.

$$A=-\frac{6}{B-2}$$

Solve for B

$$\left\{\begin{matrix}\\B=0\text{, }&\text{unconditionally}\\B=2-\frac{6}{A}\text{, }&A\neq 0\end{matrix}\right.$$