A, B, C, D, times, 4, equals, D, C, B, A

Solve for A

\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&C=0\text{ or }D=0\text{ or }B=0\end{matrix}\right.

Solve for B

\left\{\begin{matrix}\\B=0\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&C=0\text{ or }D=0\text{ or }A=0\end{matrix}\right.

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ABCD\times 4-DCBA=0

Subtract DCBA from both sides.

3ABCD=0

Combine ABCD\times 4 and -DCBA to get 3ABCD.

3BCDA=0

The equation is in standard form.

A=0

Divide 0 by 3BCD.

ABCD\times 4-DCBA=0

Subtract DCBA from both sides.

3ABCD=0

Combine ABCD\times 4 and -DCBA to get 3ABCD.

3ACDB=0

The equation is in standard form.

B=0

Divide 0 by 3ACD.

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