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

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

Simplifying
(a + b + c) + -1(b + -1a + c) + (b + -1a + c) + -1(c + -1a + -1b) = 0

Remove parenthesis around (a + b + c)
a + b + c + -1(b + -1a + c) + (b + -1a + c) + -1(c + -1a + -1b) = 0

Reorder the terms:
a + b + c + -1(-1a + b + c) + (b + -1a + c) + -1(c + -1a + -1b) = 0
a + b + c + (-1a * -1 + b * -1 + c * -1) + (b + -1a + c) + -1(c + -1a + -1b) = 0
a + b + c + (1a + -1b + -1c) + (b + -1a + c) + -1(c + -1a + -1b) = 0

Reorder the terms:
a + b + c + 1a + -1b + -1c + (-1a + b + c) + -1(c + -1a + -1b) = 0

Remove parenthesis around (-1a + b + c)
a + b + c + 1a + -1b + -1c + -1a + b + c + -1(c + -1a + -1b) = 0

Reorder the terms:
a + b + c + 1a + -1b + -1c + -1a + b + c + -1(-1a + -1b + c) = 0
a + b + c + 1a + -1b + -1c + -1a + b + c + (-1a * -1 + -1b * -1 + c * -1) = 0
a + b + c + 1a + -1b + -1c + -1a + b + c + (1a + 1b + -1c) = 0

Reorder the terms:
a + 1a + -1a + 1a + b + -1b + b + 1b + c + -1c + c + -1c = 0

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

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

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

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

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

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

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

Solving
2a + 2b = 0

Solving for variable 'a'.

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

Add '-2b' to each side of the equation.
2a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
2a + 0 = 0 + -2b
2a = 0 + -2b
Remove the zero:
2a = -2b

Divide each side by '2'.
a = -1b

Simplifying
a = -1b