(AX+B)C=D

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Solution for (AX+B)C=D equation: 


Simplifying
(AX + B) * C = D

Reorder the terms for easier multiplication:
C(AX + B) = D
(AX * C + B * C) = D
(ACX + BC) = D

Solving
ACX + BC = D

Solving for variable 'A'.

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

Add '-1BC' to each side of the equation.
ACX + BC + -1BC = -1BC + D

Combine like terms: BC + -1BC = 0
ACX + 0 = -1BC + D
ACX = -1BC + D

Divide each side by 'CX'.
A = -1BX-1 + C-1DX-1

Simplifying
A = -1BX-1 + C-1DX-1

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