3a^2b^2-5ab-22=

Solution for 3a^2b^2-5ab-22= equation:

Simplifying
3a2b2 + -5ab + -22 = 0

Reorder the terms:
-22 + -5ab + 3a2b2 = 0

Solving
-22 + -5ab + 3a2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -1ab)(11 + -3ab) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(11 + -3ab)' equal to zero and attempt to solve:

Simplifying
11 + -3ab = 0

Solving
11 + -3ab = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3ab = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3ab = 0 + -11
-3ab = 0 + -11

Combine like terms: 0 + -11 = -11
-3ab = -11

Divide each side by '-3b'.
a = 3.666666667b-1

Simplifying
a = 3.666666667b-1
Solution
a = {-2b-1, 3.666666667b-1}