(ab)+(cd)=(a+b)(c+d)

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Solution for (ab)+(cd)=(a+b)(c+d) equation: 


Simplifying
(ab) + (cd) = (a + b)(c + d)
ab + (cd) = (a + b)(c + d)
ab + cd = (a + b)(c + d)

Multiply (a + b) * (c + d)
ab + cd = (a(c + d) + b(c + d))
ab + cd = ((c * a + d * a) + b(c + d))
ab + cd = ((ac + ad) + b(c + d))
ab + cd = (ac + ad + (c * b + d * b))
ab + cd = (ac + ad + (bc + bd))
ab + cd = (ac + ad + bc + bd)

Solving
ab + cd = ac + ad + bc + bd

Solving for variable 'a'.

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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