(x+y)+(z+w)=x+(y+(z+w))

Solution for (x+y)+(z+w)=x+(y+(z+w)) equation:

Simplifying
(x + y) + (z + w) = x + (y + (z + w))

Remove parenthesis around (x + y)
x + y + (z + w) = x + (y + (z + w))

Reorder the terms:
x + y + (w + z) = x + (y + (z + w))

Remove parenthesis around (w + z)
x + y + w + z = x + (y + (z + w))

Reorder the terms:
w + x + y + z = x + (y + (z + w))

Reorder the terms:
w + x + y + z = x + (y + (w + z))

Remove parenthesis around (w + z)
w + x + y + z = x + (y + w + z)

Reorder the terms:
w + x + y + z = x + (w + y + z)

Remove parenthesis around (w + y + z)
w + x + y + z = x + w + y + z

Reorder the terms:
w + x + y + z = w + x + y + z

Add '-1w' to each side of the equation.
w + x + y + -1w + z = w + x + y + -1w + z

Reorder the terms:
w + -1w + x + y + z = w + x + y + -1w + z

Combine like terms: w + -1w = 0
0 + x + y + z = w + x + y + -1w + z
x + y + z = w + x + y + -1w + z

Reorder the terms:
x + y + z = w + -1w + x + y + z

Combine like terms: w + -1w = 0
x + y + z = 0 + x + y + z
x + y + z = x + y + z

Add '-1x' to each side of the equation.
x + y + -1x + z = x + y + -1x + z

Reorder the terms:
x + -1x + y + z = x + y + -1x + z

Combine like terms: x + -1x = 0
0 + y + z = x + y + -1x + z
y + z = x + y + -1x + z

Reorder the terms:
y + z = x + -1x + y + z

Combine like terms: x + -1x = 0
y + z = 0 + y + z
y + z = y + z

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

Combine like terms: y + -1y = 0
0 + z = y + -1y + z
z = y + -1y + z

Combine like terms: y + -1y = 0
z = 0 + z
z = z

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

Combine like terms: z + -1z = 0
0 = z + -1z

Combine like terms: z + -1z = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.