(1+-1a)(1+-1b)(1+-1c)=x

Solution for (1+-1a)(1+-1b)(1+-1c)=x equation:

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

Multiply (1 + -1a) * (1 + -1b)
(1(1 + -1b) + -1a * (1 + -1b))(1 + -1c) = x
((1 * 1 + -1b * 1) + -1a * (1 + -1b))(1 + -1c) = x
((1 + -1b) + -1a * (1 + -1b))(1 + -1c) = x
(1 + -1b + (1 * -1a + -1b * -1a))(1 + -1c) = x
(1 + -1b + (-1a + 1ab))(1 + -1c) = x

Reorder the terms:
(1 + -1a + 1ab + -1b)(1 + -1c) = x
(1 + -1a + 1ab + -1b)(1 + -1c) = x

Multiply (1 + -1a + 1ab + -1b) * (1 + -1c)
(1(1 + -1c) + -1a * (1 + -1c) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = x
((1 * 1 + -1c * 1) + -1a * (1 + -1c) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = x
((1 + -1c) + -1a * (1 + -1c) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = x
(1 + -1c + (1 * -1a + -1c * -1a) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = x
(1 + -1c + (-1a + 1ac) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = x
(1 + -1c + -1a + 1ac + (1 * 1ab + -1c * 1ab) + -1b * (1 + -1c)) = x
(1 + -1c + -1a + 1ac + (1ab + -1abc) + -1b * (1 + -1c)) = x
(1 + -1c + -1a + 1ac + 1ab + -1abc + (1 * -1b + -1c * -1b)) = x
(1 + -1c + -1a + 1ac + 1ab + -1abc + (-1b + 1bc)) = x

Reorder the terms:
(1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c) = x
(1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c) = x

Solving
1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = x

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1 + -1c = -1 + x

Reorder the terms:
1 + -1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = -1 + x

Combine like terms: 1 + -1 = 0
0 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = -1 + x
-1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = -1 + x

Add 'b' to each side of the equation.
-1a + 1ab + -1abc + 1ac + -1b + 1bc + b + -1c = -1 + b + x

Reorder the terms:
-1a + 1ab + -1abc + 1ac + -1b + b + 1bc + -1c = -1 + b + x

Combine like terms: -1b + b = 0
-1a + 1ab + -1abc + 1ac + 0 + 1bc + -1c = -1 + b + x
-1a + 1ab + -1abc + 1ac + 1bc + -1c = -1 + b + x

Add '-1bc' to each side of the equation.
-1a + 1ab + -1abc + 1ac + 1bc + -1bc + -1c = -1 + b + -1bc + x

Combine like terms: 1bc + -1bc = 0
-1a + 1ab + -1abc + 1ac + 0 + -1c = -1 + b + -1bc + x
-1a + 1ab + -1abc + 1ac + -1c = -1 + b + -1bc + x

Add 'c' to each side of the equation.
-1a + 1ab + -1abc + 1ac + -1c + c = -1 + b + -1bc + c + x

Combine like terms: -1c + c = 0
-1a + 1ab + -1abc + 1ac + 0 = -1 + b + -1bc + c + x
-1a + 1ab + -1abc + 1ac = -1 + b + -1bc + c + x

Reorder the terms:
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = -1 + b + -1bc + c + x + 1 + -1b + bc + -1c + -1x

Reorder the terms:
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = -1 + 1 + b + -1b + -1bc + bc + c + -1c + x + -1x

Combine like terms: -1 + 1 = 0
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = 0 + b + -1b + -1bc + bc + c + -1c + x + -1x
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = b + -1b + -1bc + bc + c + -1c + x + -1x

Combine like terms: b + -1b = 0
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = 0 + -1bc + bc + c + -1c + x + -1x
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = -1bc + bc + c + -1c + x + -1x

Combine like terms: -1bc + bc = 0
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = 0 + c + -1c + x + -1x
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = c + -1c + x + -1x

Combine like terms: c + -1c = 0
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = 0 + x + -1x
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = x + -1x

Combine like terms: x + -1x = 0
1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c + -1x = 0

The solution to this equation could not be determined.