-6a+48ab+12a^2b=2ab

Solution for -6a+48ab+12a^2b=2ab equation:

Simplifying
-6a + 48ab + 12a2b = 2ab

Solving
-6a + 48ab + 12a2b = 2ab

Solving for variable 'a'.

Reorder the terms:
-6a + 48ab + -2ab + 12a2b = 2ab + -2ab

Combine like terms: 48ab + -2ab = 46ab
-6a + 46ab + 12a2b = 2ab + -2ab

Combine like terms: 2ab + -2ab = 0
-6a + 46ab + 12a2b = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-3 + 23b + 6ab) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-3 + 23b + 6ab)' equal to zero and attempt to solve:

Simplifying
-3 + 23b + 6ab = 0

Reorder the terms:
-3 + 6ab + 23b = 0

Solving
-3 + 6ab + 23b = 0

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

Add '3' to each side of the equation.
-3 + 6ab + 3 + 23b = 0 + 3

Reorder the terms:
-3 + 3 + 6ab + 23b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6ab + 23b = 0 + 3
6ab + 23b = 0 + 3

Combine like terms: 0 + 3 = 3
6ab + 23b = 3

Add '-23b' to each side of the equation.
6ab + 23b + -23b = 3 + -23b

Combine like terms: 23b + -23b = 0
6ab + 0 = 3 + -23b
6ab = 3 + -23b

Divide each side by '6b'.
a = 0.5b-1 + -3.833333333

Simplifying
a = 0.5b-1 + -3.833333333

Reorder the terms:
a = -3.833333333 + 0.5b-1
Solution
a = {0, -3.833333333 + 0.5b-1}