[(a+3b)-a]-[a-(a-3b)]=0

Solution for [(a+3b)-a]-[a-(a-3b)]=0 equation:

Simplifying
[(a + 3b) + -1a] + -1[a + -1(a + -3b)] = 0

Remove parenthesis around (a + 3b)
[a + 3b + -1a] + -1[a + -1(a + -3b)] = 0

Reorder the terms:
[a + -1a + 3b] + -1[a + -1(a + -3b)] = 0

Combine like terms: a + -1a = 0
[0 + 3b] + -1[a + -1(a + -3b)] = 0
[3b] + -1[a + -1(a + -3b)] = 0
[3b] + -1[a + -1(a + -3b)] = 0
[3b] + -1[a + (a * -1 + -3b * -1)] = 0
[3b] + -1[a + (-1a + 3b)] = 0

Combine like terms: a + -1a = 0
[3b] + -1[0 + 3b] = 0
[3b] + -1[3b] = 0

Remove brackets around [3b]
[3b] + -1 * 3b = 0

Multiply -1 * 3
[3b] + -3b = 0

Combine like terms: [3b] + -3b = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.