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

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

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

Remove parenthesis around (a + -1b)
a + -1b + -1(c + d) = (a + c) + -1(b + d)
a + -1b + (c * -1 + d * -1) = (a + c) + -1(b + d)
a + -1b + (-1c + -1d) = (a + c) + -1(b + d)

Remove parenthesis around (a + c)
a + -1b + -1c + -1d = a + c + -1(b + d)
a + -1b + -1c + -1d = a + c + (b * -1 + d * -1)
a + -1b + -1c + -1d = a + c + (-1b + -1d)

Reorder the terms:
a + -1b + -1c + -1d = a + -1b + c + -1d

Add '-1a' to each side of the equation.
a + -1b + -1c + -1a + -1d = a + -1b + c + -1a + -1d

Reorder the terms:
a + -1a + -1b + -1c + -1d = a + -1b + c + -1a + -1d

Combine like terms: a + -1a = 0
0 + -1b + -1c + -1d = a + -1b + c + -1a + -1d
-1b + -1c + -1d = a + -1b + c + -1a + -1d

Reorder the terms:
-1b + -1c + -1d = a + -1a + -1b + c + -1d

Combine like terms: a + -1a = 0
-1b + -1c + -1d = 0 + -1b + c + -1d
-1b + -1c + -1d = -1b + c + -1d

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

Reorder the terms:
-1b + b + -1c + -1d = -1b + c + b + -1d

Combine like terms: -1b + b = 0
0 + -1c + -1d = -1b + c + b + -1d
-1c + -1d = -1b + c + b + -1d

Reorder the terms:
-1c + -1d = -1b + b + c + -1d

Combine like terms: -1b + b = 0
-1c + -1d = 0 + c + -1d
-1c + -1d = c + -1d

Add 'd' to each side of the equation.
-1c + -1d + d = c + -1d + d

Combine like terms: -1d + d = 0
-1c + 0 = c + -1d + d
-1c = c + -1d + d

Combine like terms: -1d + d = 0
-1c = c + 0
-1c = c

Solving
-1c = c

Solving for variable 'c'.

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

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

Combine like terms: -1c + -1c = -2c
-2c = c + -1c

Combine like terms: c + -1c = 0
-2c = 0

Divide each side by '-2'.
c = 0

Simplifying
c = 0