a*b=(a-c)*(b+d)

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Solution for a*b=(a-c)*(b+d) equation: 


Simplifying
a * b = (a + -1c)(b + d)

Multiply a * b
ab = (a + -1c)(b + d)

Multiply (a + -1c) * (b + d)
ab = (a(b + d) + -1c * (b + d))
ab = ((b * a + d * a) + -1c * (b + d))
ab = ((ab + ad) + -1c * (b + d))
ab = (ab + ad + (b * -1c + d * -1c))
ab = (ab + ad + (-1bc + -1cd))
ab = (ab + ad + -1bc + -1cd)

Add '-1ab' to each side of the equation.
ab + -1ab = ab + ad + -1bc + -1ab + -1cd

Combine like terms: ab + -1ab = 0
0 = ab + ad + -1bc + -1ab + -1cd

Reorder the terms:
0 = ab + -1ab + ad + -1bc + -1cd

Combine like terms: ab + -1ab = 0
0 = 0 + ad + -1bc + -1cd
0 = ad + -1bc + -1cd

Solving
0 = ad + -1bc + -1cd

Solving for variable 'a'.

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

Add '-1ad' to each side of the equation.
0 + -1ad = ad + -1bc + -1ad + -1cd
Remove the zero:
-1ad = ad + -1bc + -1ad + -1cd

Reorder the terms:
-1ad = ad + -1ad + -1bc + -1cd

Combine like terms: ad + -1ad = 0
-1ad = 0 + -1bc + -1cd
-1ad = -1bc + -1cd

Divide each side by '-1d'.
a = bcd-1 + c

Simplifying
a = bcd-1 + c

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