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

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


Simplifying
1 = [1 + -1(y + z)] + [1 + -1(x + z)] + [1 + -1(x + y)]
1 = [1 + (y * -1 + z * -1)] + [1 + -1(x + z)] + [1 + -1(x + y)]
1 = [1 + (-1y + -1z)] + [1 + -1(x + z)] + [1 + -1(x + y)]

Remove brackets around [1 + -1y + -1z]
1 = 1 + -1y + -1z + [1 + -1(x + z)] + [1 + -1(x + y)]
1 = 1 + -1y + -1z + [1 + (x * -1 + z * -1)] + [1 + -1(x + y)]
1 = 1 + -1y + -1z + [1 + (-1x + -1z)] + [1 + -1(x + y)]

Remove brackets around [1 + -1x + -1z]
1 = 1 + -1y + -1z + 1 + -1x + -1z + [1 + -1(x + y)]
1 = 1 + -1y + -1z + 1 + -1x + -1z + [1 + (x * -1 + y * -1)]
1 = 1 + -1y + -1z + 1 + -1x + -1z + [1 + (-1x + -1y)]

Remove brackets around [1 + -1x + -1y]
1 = 1 + -1y + -1z + 1 + -1x + -1z + 1 + -1x + -1y

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

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

Combine like terms: 2 + 1 = 3
1 = 3 + -1x + -1x + -1y + -1y + -1z + -1z

Combine like terms: -1x + -1x = -2x
1 = 3 + -2x + -1y + -1y + -1z + -1z

Combine like terms: -1y + -1y = -2y
1 = 3 + -2x + -2y + -1z + -1z

Combine like terms: -1z + -1z = -2z
1 = 3 + -2x + -2y + -2z

Solving
1 = 3 + -2x + -2y + -2z

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
1 + 2x = 3 + -2x + -2y + 2x + -2z

Reorder the terms:
1 + 2x = 3 + -2x + 2x + -2y + -2z

Combine like terms: -2x + 2x = 0
1 + 2x = 3 + 0 + -2y + -2z
1 + 2x = 3 + -2y + -2z

Add '-1' to each side of the equation.
1 + -1 + 2x = 3 + -2y + -1 + -2z

Combine like terms: 1 + -1 = 0
0 + 2x = 3 + -2y + -1 + -2z
2x = 3 + -2y + -1 + -2z

Reorder the terms:
2x = 3 + -1 + -2y + -2z

Combine like terms: 3 + -1 = 2
2x = 2 + -2y + -2z

Divide each side by '2'.
x = 1 + -1y + -1z

Simplifying
x = 1 + -1y + -1z

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