12a^2b+13ab-4b=0

Solution for 12a^2b+13ab-4b=0 equation:

Simplifying
12a2b + 13ab + -4b = 0

Reorder the terms:
13ab + 12a2b + -4b = 0

Solving
13ab + 12a2b + -4b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b'.
b(13a + 12a2 + -4) = 0

Factor a trinomial.
b((4a + -1)(3a + 4)) = 0

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

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4a + -1)' equal to zero and attempt to solve:

Simplifying
4a + -1 = 0

Reorder the terms:
-1 + 4a = 0

Solving
-1 + 4a = 0

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

Add '1' to each side of the equation.
-1 + 1 + 4a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4a = 0 + 1
4a = 0 + 1

Combine like terms: 0 + 1 = 1
4a = 1

Divide each side by '4'.
a = 0.25

Simplifying
a = 0.25
Subproblem 3
Set the factor '(3a + 4)' equal to zero and attempt to solve:

Simplifying
3a + 4 = 0

Reorder the terms:
4 + 3a = 0

Solving
4 + 3a = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3a = 0 + -4

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

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

Divide each side by '3'.
a = -1.333333333

Simplifying
a = -1.333333333
Solution
a = {0.25, -1.333333333}