D(a-b)=(c-b)

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Solution for D(a-b)=(c-b) equation: 


Simplifying
D(a + -1b) = (c + -1b)
(a * D + -1b * D) = (c + -1b)
(aD + -1bD) = (c + -1b)

Reorder the terms:
aD + -1bD = (-1b + c)

Remove parenthesis around (-1b + c)
aD + -1bD = -1b + c

Solving
aD + -1bD = -1b + c

Solving for variable 'a'.

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

Add 'bD' to each side of the equation.
aD + -1bD + bD = -1b + bD + c

Combine like terms: -1bD + bD = 0
aD + 0 = -1b + bD + c
aD = -1b + bD + c

Divide each side by 'D'.
a = -1bD-1 + b + cD-1

Simplifying
a = -1bD-1 + b + cD-1

Reorder the terms:
a = b + -1bD-1 + cD-1

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