a + b + 2c + |a-b| + |a + b - 2c + |a-b| |
The solution splits into two cases
If a>=b then a + b + 2c + a - b + |a + b - 2c + a - b|
If a<=b then a + b + 2c + b - a + |a + b - 2c + b - a|
The first one:
If a>=b then a + b + 2c + a - b + |a + b - 2c + a - b|
2a + 2c + |2a - 2c|
2a + 2c +2|a-c|
The first one splits again:
If a>=c then 2a + 2c + 2a - 2c = 4a
If a<=c then 2a + 2c + 2c - 2a = 4c
The second one:
If a<=b then a + b + 2c + b - a + |a + b - 2c + b - a|
2b + 2c + |2b - 2c|
2b + 2c + 2|b - c|
The second one splits again too:
If b>=c then 2b + 2c + 2b - 2c = 4b
If b<=c then 2b + 2c + 2c - 2b = 4c
Two sets of two solutions each, for a total of four solutions:
If a>=b and a>=c then the problem simplifies to 4a
If a>=b and a<=c then the problem simplifies to 4c
If a<=b and b>=c then the problem simplifies to 4b
If a<=b and b<=c then the problem simplifies to 4c