a^2b^2+7ab+12=0

Solution for a^2b^2+7ab+12=0 equation:

Simplifying
a2b2 + 7ab + 12 = 0

Reorder the terms:
12 + 7ab + a2b2 = 0

Solving
12 + 7ab + a2b2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(4 + ab)' equal to zero and attempt to solve:

Simplifying
4 + ab = 0

Solving
4 + ab = 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 + ab = 0 + -4

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

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

Divide each side by 'b'.
a = -4b-1

Simplifying
a = -4b-1
Subproblem 2
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
Solution
a = {-4b-1, -3b-1}