3(a+b)-2(a-b)=0

Solution for 3(a+b)-2(a-b)=0 equation:

Simplifying
3(a + b) + -2(a + -1b) = 0
(a * 3 + b * 3) + -2(a + -1b) = 0
(3a + 3b) + -2(a + -1b) = 0
3a + 3b + (a * -2 + -1b * -2) = 0
3a + 3b + (-2a + 2b) = 0

Reorder the terms:
3a + -2a + 3b + 2b = 0

Combine like terms: 3a + -2a = 1a
1a + 3b + 2b = 0

Combine like terms: 3b + 2b = 5b
1a + 5b = 0

Solving
1a + 5b = 0

Solving for variable 'a'.

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

Add '-5b' to each side of the equation.
1a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
1a + 0 = 0 + -5b
1a = 0 + -5b
Remove the zero:
1a = -5b

Divide each side by '1'.
a = -5b

Simplifying
a = -5b