(a+b)(c+d)=(2ab)(cd)

Solution for (a+b)(c+d)=(2ab)(cd) equation:

Simplifying
(a + b)(c + d) = (2ab)(cd)

Multiply (a + b) * (c + d)
(a(c + d) + b(c + d)) = (2ab)(cd)
((c * a + d * a) + b(c + d)) = (2ab)(cd)
((ac + ad) + b(c + d)) = (2ab)(cd)
(ac + ad + (c * b + d * b)) = (2ab)(cd)
(ac + ad + (bc + bd)) = (2ab)(cd)
(ac + ad + bc + bd) = (2ab)(cd)

Remove parenthesis around (2ab)
ac + ad + bc + bd = 2ab(cd)

Multiply ab * cd
ac + ad + bc + bd = 2abcd

Solving
ac + ad + bc + bd = 2abcd

Solving for variable 'a'.

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

Add '-2abcd' to each side of the equation.
ac + ad + bc + -2abcd + bd = 2abcd + -2abcd

Reorder the terms:
-2abcd + ac + ad + bc + bd = 2abcd + -2abcd

Combine like terms: 2abcd + -2abcd = 0
-2abcd + ac + ad + bc + bd = 0

Add '-1bc' to each side of the equation.
-2abcd + ac + ad + bc + -1bc + bd = 0 + -1bc

Combine like terms: bc + -1bc = 0
-2abcd + ac + ad + 0 + bd = 0 + -1bc
-2abcd + ac + ad + bd = 0 + -1bc
Remove the zero:
-2abcd + ac + ad + bd = -1bc

Add '-1bd' to each side of the equation.
-2abcd + ac + ad + bd + -1bd = -1bc + -1bd

Combine like terms: bd + -1bd = 0
-2abcd + ac + ad + 0 = -1bc + -1bd
-2abcd + ac + ad = -1bc + -1bd

Reorder the terms:
-2abcd + ac + ad + bc + bd = -1bc + bc + -1bd + bd

Combine like terms: -1bc + bc = 0
-2abcd + ac + ad + bc + bd = 0 + -1bd + bd
-2abcd + ac + ad + bc + bd = -1bd + bd

Combine like terms: -1bd + bd = 0
-2abcd + ac + ad + bc + bd = 0

The solution to this equation could not be determined.