a^2b^2+5ab+6=0

Solution for a^2b^2+5ab+6=0 equation:

Simplifying
a2b2 + 5ab + 6 = 0

Reorder the terms:
6 + 5ab + a2b2 = 0

Solving
6 + 5ab + a2b2 = 0

Solving for variable 'a'.

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

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

Simplifying
3 + ab = 0

Solving
3 + ab = 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 + ab = 0 + -3

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

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

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

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

Simplifying
2 + ab = 0

Solving
2 + ab = 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 + ab = 0 + -2

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

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

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

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