(A-B)X(C-D)=x

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Solution for (A-B)X(C-D)=x equation: 


Simplifying
(A + -1B) * X(C + -1D) = x

Reorder the terms for easier multiplication:
X(A + -1B)(C + -1D) = x

Multiply (A + -1B) * (C + -1D)
X(A(C + -1D) + -1B * (C + -1D)) = x
X((C * A + -1D * A) + -1B * (C + -1D)) = x
X((AC + -1AD) + -1B * (C + -1D)) = x
X(AC + -1AD + (C * -1B + -1D * -1B)) = x
X(AC + -1AD + (-1BC + 1BD)) = x
X(AC + -1AD + -1BC + 1BD) = x
(AC * X + -1AD * X + -1BC * X + 1BD * X) = x
(ACX + -1ADX + -1BCX + 1BDX) = x

Solving
ACX + -1ADX + -1BCX + 1BDX = x

Solving for variable 'A'.

Move all terms containing A to the left, all other terms to the right.

Add 'BCX' to each side of the equation.
ACX + -1ADX + -1BCX + BCX + 1BDX = BCX + x

Combine like terms: -1BCX + BCX = 0
ACX + -1ADX + 0 + 1BDX = BCX + x
ACX + -1ADX + 1BDX = BCX + x

Add '-1BDX' to each side of the equation.
ACX + -1ADX + 1BDX + -1BDX = BCX + -1BDX + x

Combine like terms: 1BDX + -1BDX = 0
ACX + -1ADX + 0 = BCX + -1BDX + x
ACX + -1ADX = BCX + -1BDX + x

Reorder the terms:
ACX + -1ADX + -1BCX + BDX + -1x = BCX + -1BCX + -1BDX + BDX + x + -1x

Combine like terms: BCX + -1BCX = 0
ACX + -1ADX + -1BCX + BDX + -1x = 0 + -1BDX + BDX + x + -1x
ACX + -1ADX + -1BCX + BDX + -1x = -1BDX + BDX + x + -1x

Combine like terms: -1BDX + BDX = 0
ACX + -1ADX + -1BCX + BDX + -1x = 0 + x + -1x
ACX + -1ADX + -1BCX + BDX + -1x = x + -1x

Combine like terms: x + -1x = 0
ACX + -1ADX + -1BCX + BDX + -1x = 0

The solution to this equation could not be determined.

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