3a+4b=2a+ab+a+3ab

Solution for 3a+4b=2a+ab+a+3ab equation:

Simplifying
3a + 4b = 2a + ab + a + 3ab

Reorder the terms:
3a + 4b = 2a + a + ab + 3ab

Combine like terms: 2a + a = 3a
3a + 4b = 3a + ab + 3ab

Combine like terms: ab + 3ab = 4ab
3a + 4b = 3a + 4ab

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

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

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

Solving
4b = 4ab

Solving for variable 'b'.

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

Add '-4ab' to each side of the equation.
-4ab + 4b = 4ab + -4ab

Combine like terms: 4ab + -4ab = 0
-4ab + 4b = 0

Factor out the Greatest Common Factor (GCF), '4b'.
4b(-1a + 1) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(-1a + 1)' equal to zero and attempt to solve:

Simplifying
-1a + 1 = 0

Reorder the terms:
1 + -1a = 0

Solving
1 + -1a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

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

Combine like terms: -1a + a = 0
0 = -1 + a

Simplifying
0 = -1 + a

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}