7a^2b^2+13ab+6=0

Solution for 7a^2b^2+13ab+6=0 equation:

Simplifying
7a2b2 + 13ab + 6 = 0

Reorder the terms:
6 + 13ab + 7a2b2 = 0

Solving
6 + 13ab + 7a2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + ab)(6 + 7ab) = 0

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

Simplifying
1 + ab = 0

Solving
1 + ab = 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 + ab = 0 + -1

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

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

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

Simplifying
a = -1b-1
Subproblem 2
Set the factor '(6 + 7ab)' equal to zero and attempt to solve:

Simplifying
6 + 7ab = 0

Solving
6 + 7ab = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7ab = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7ab = 0 + -6
7ab = 0 + -6

Combine like terms: 0 + -6 = -6
7ab = -6

Divide each side by '7b'.
a = -0.8571428571b-1

Simplifying
a = -0.8571428571b-1
Solution
a = {-1b-1, -0.8571428571b-1}