=(x+y-1)+(x+y+1)-(x+y-z)

Solution for =(x+y-1)+(x+y+1)-(x+y-z) equation:

Simplifying
0 = (x + y + -1) + (x + y + 1) + -1(x + y + -1z)

Reorder the terms:
0 = (-1 + x + y) + (x + y + 1) + -1(x + y + -1z)

Remove parenthesis around (-1 + x + y)
0 = -1 + x + y + (x + y + 1) + -1(x + y + -1z)

Reorder the terms:
0 = -1 + x + y + (1 + x + y) + -1(x + y + -1z)

Remove parenthesis around (1 + x + y)
0 = -1 + x + y + 1 + x + y + -1(x + y + -1z)
0 = -1 + x + y + 1 + x + y + (x * -1 + y * -1 + -1z * -1)
0 = -1 + x + y + 1 + x + y + (-1x + -1y + 1z)

Reorder the terms:
0 = -1 + 1 + x + x + -1x + y + y + -1y + 1z

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

Combine like terms: x + x = 2x
0 = 2x + -1x + y + y + -1y + 1z

Combine like terms: 2x + -1x = 1x
0 = 1x + y + y + -1y + 1z

Combine like terms: y + y = 2y
0 = 1x + 2y + -1y + 1z

Combine like terms: 2y + -1y = 1y
0 = 1x + 1y + 1z

Solving
0 = 1x + 1y + 1z

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
0 + -1x = 1x + 1y + -1x + 1z
Remove the zero:
-1x = 1x + 1y + -1x + 1z

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

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

Divide each side by '-1'.
x = -1y + -1z

Simplifying
x = -1y + -1z