Ab+cd=ac+Bd

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Solution for Ab+cd=ac+Bd equation: 


Simplifying
Ab + cd = ac + Bd

Solving
bA + cd = ac + dB

Solving for variable 'b'.

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

Add '-1cd' to each side of the equation.
bA + cd + -1cd = ac + -1cd + dB

Combine like terms: cd + -1cd = 0
bA + 0 = ac + -1cd + dB
bA = ac + -1cd + dB

Divide each side by 'A'.
b = acA-1 + -1cdA-1 + dA-1B

Simplifying
b = acA-1 + -1cdA-1 + dA-1B

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