Solve ABA-AB=378

$$A B A - A B = 378$$

Solve for B

$$B=\frac{378}{A\left(A-1\right)}$$

$$A\neq 1\text{ and }A\neq 0$$

Steps for Solving Linear Equation

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

$$A^{2}B-AB=378$$

Combine all terms containing B.

$$\left(A^{2}-A\right)B=378$$

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

$$\frac{\left(A^{2}-A\right)B}{A^{2}-A}=\frac{378}{A^{2}-A}$$

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

$$B=\frac{378}{A^{2}-A}$$

Divide 378 by A^{2}-A.

$$B=\frac{378}{A\left(A-1\right)}$$

Solve for A

$$A=\frac{\sqrt{B\left(B+1512\right)}+B}{2B}$$

$$A=\frac{-\sqrt{B\left(B+1512\right)}+B}{2B}\text{, }B>0\text{ or }B\leq -1512$$