ab(14a^2b^2-33ab-5)=0

Solution for ab(14a^2b^2-33ab-5)=0 equation:

Simplifying
ab(14a2b2 + -33ab + -5) = 0

Reorder the terms:
ab(-5 + -33ab + 14a2b2) = 0
(-5 * ab + -33ab * ab + 14a2b2 * ab) = 0
(-5ab + -33a2b2 + 14a3b3) = 0

Solving
-5ab + -33a2b2 + 14a3b3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(-5 + -33ab + 14a2b2) = 0

Factor a trinomial.
ab((-1 + -7ab)(5 + -2ab)) = 0

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

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + -7ab)' equal to zero and attempt to solve:

Simplifying
-1 + -7ab = 0

Solving
-1 + -7ab = 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 + -7ab = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7ab = 0 + 1
-7ab = 0 + 1

Combine like terms: 0 + 1 = 1
-7ab = 1

Divide each side by '-7b'.
a = -0.1428571429b-1

Simplifying
a = -0.1428571429b-1
Subproblem 3
Set the factor '(5 + -2ab)' equal to zero and attempt to solve:

Simplifying
5 + -2ab = 0

Solving
5 + -2ab = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2ab = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2ab = 0 + -5
-2ab = 0 + -5

Combine like terms: 0 + -5 = -5
-2ab = -5

Divide each side by '-2b'.
a = 2.5b-1

Simplifying
a = 2.5b-1
Solution
a = {-0.1428571429b-1, 2.5b-1}