A(x+b)=c(x+d)

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Solution for A(x+b)=c(x+d) equation: 


Simplifying
A(x + b) = c(x + d)

Reorder the terms:
A(b + x) = c(x + d)
(b * A + x * A) = c(x + d)
(bA + xA) = c(x + d)

Reorder the terms:
bA + xA = c(d + x)
bA + xA = (d * c + x * c)
bA + xA = (cd + cx)

Solving
bA + xA = cd + cx

Solving for variable 'b'.

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

Add '-1xA' to each side of the equation.
bA + xA + -1xA = cd + cx + -1xA

Combine like terms: xA + -1xA = 0
bA + 0 = cd + cx + -1xA
bA = cd + cx + -1xA

Divide each side by 'A'.
b = cdA-1 + cxA-1 + -1x

Simplifying
b = cdA-1 + cxA-1 + -1x

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