[(3ab+2)-1][(3ab+2)+1]=

Solution for [(3ab+2)-1][(3ab+2)+1]= equation:

Simplifying
[(3ab + 2) + -1][(3ab + 2) + 1] = 0

Reorder the terms:
[(2 + 3ab) + -1][(3ab + 2) + 1] = 0

Remove parenthesis around (2 + 3ab)
[2 + 3ab + -1][(3ab + 2) + 1] = 0

Reorder the terms:
[2 + -1 + 3ab][(3ab + 2) + 1] = 0

Combine like terms: 2 + -1 = 1
[1 + 3ab][(3ab + 2) + 1] = 0

Reorder the terms:
[1 + 3ab][(2 + 3ab) + 1] = 0

Remove parenthesis around (2 + 3ab)
[1 + 3ab][2 + 3ab + 1] = 0

Reorder the terms:
[1 + 3ab][2 + 1 + 3ab] = 0

Combine like terms: 2 + 1 = 3
[1 + 3ab][3 + 3ab] = 0

Multiply [1 + 3ab] * [3 + 3ab]
[1[3 + 3ab] + 3ab * [3 + 3ab]] = 0
[[3 * 1 + 3ab * 1] + 3ab * [3 + 3ab]] = 0
[[3 + 3ab] + 3ab * [3 + 3ab]] = 0
[3 + 3ab + [3 * 3ab + 3ab * 3ab]] = 0
[3 + 3ab + [9ab + 9a2b2]] = 0

Combine like terms: 3ab + 9ab = 12ab
[3 + 12ab + 9a2b2] = 0

Solving
3 + 12ab + 9a2b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 4ab + 3a2b2) = 0

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

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

Simplifying
1 + 3ab = 0

Solving
1 + 3ab = 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 + 3ab = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3ab = 0 + -1
3ab = 0 + -1

Combine like terms: 0 + -1 = -1
3ab = -1

Divide each side by '3b'.
a = -0.3333333333b-1

Simplifying
a = -0.3333333333b-1
Solution
a = {-1b-1, -0.3333333333b-1}