a^2b^2+ab-6=0

Solution for a^2b^2+ab-6=0 equation:

Simplifying
a2b2 + ab + -6 = 0

Reorder the terms:
-6 + ab + a2b2 = 0

Solving
-6 + ab + a2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1ab)(2 + -1ab) = 0

Subproblem 1
Set the factor '(-3 + -1ab)' equal to zero and attempt to solve:

Simplifying
-3 + -1ab = 0

Solving
-3 + -1ab = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1ab = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1ab = 0 + 3
-1ab = 0 + 3

Combine like terms: 0 + 3 = 3
-1ab = 3

Divide each side by '-1b'.
a = -3b-1

Simplifying
a = -3b-1
Subproblem 2
Set the factor '(2 + -1ab)' equal to zero and attempt to solve:

Simplifying
2 + -1ab = 0

Solving
2 + -1ab = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1ab = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1ab = 0 + -2
-1ab = 0 + -2

Combine like terms: 0 + -2 = -2
-1ab = -2

Divide each side by '-1b'.
a = 2b-1

Simplifying
a = 2b-1
Solution
a = {-3b-1, 2b-1}