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

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

Simplifying
2(a + 2b) + -1(a + -3b) = 0
(a * 2 + 2b * 2) + -1(a + -3b) = 0
(2a + 4b) + -1(a + -3b) = 0
2a + 4b + (a * -1 + -3b * -1) = 0
2a + 4b + (-1a + 3b) = 0

Reorder the terms:
2a + -1a + 4b + 3b = 0

Combine like terms: 2a + -1a = 1a
1a + 4b + 3b = 0

Combine like terms: 4b + 3b = 7b
1a + 7b = 0

Solving
1a + 7b = 0

Solving for variable 'a'.

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

Add '-7b' to each side of the equation.
1a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
1a + 0 = 0 + -7b
1a = 0 + -7b
Remove the zero:
1a = -7b

Divide each side by '1'.
a = -7b

Simplifying
a = -7b