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

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

Simplifying
2b + 2(3 + 2a) = 3(a + b)
2b + (3 * 2 + 2a * 2) = 3(a + b)
2b + (6 + 4a) = 3(a + b)

Reorder the terms:
6 + 4a + 2b = 3(a + b)
6 + 4a + 2b = (a * 3 + b * 3)
6 + 4a + 2b = (3a + 3b)

Solving
6 + 4a + 2b = 3a + 3b

Solving for variable 'a'.

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

Add '-3a' to each side of the equation.
6 + 4a + -3a + 2b = 3a + -3a + 3b

Combine like terms: 4a + -3a = 1a
6 + 1a + 2b = 3a + -3a + 3b

Combine like terms: 3a + -3a = 0
6 + 1a + 2b = 0 + 3b
6 + 1a + 2b = 3b

Add '-6' to each side of the equation.
6 + 1a + -6 + 2b = -6 + 3b

Reorder the terms:
6 + -6 + 1a + 2b = -6 + 3b

Combine like terms: 6 + -6 = 0
0 + 1a + 2b = -6 + 3b
1a + 2b = -6 + 3b

Add '-2b' to each side of the equation.
1a + 2b + -2b = -6 + 3b + -2b

Combine like terms: 2b + -2b = 0
1a + 0 = -6 + 3b + -2b
1a = -6 + 3b + -2b

Combine like terms: 3b + -2b = 1b
1a = -6 + 1b

Divide each side by '1'.
a = -6 + 1b

Simplifying
a = -6 + 1b