27a^2b^2+42ab+8=0

Solution for 27a^2b^2+42ab+8=0 equation:

Simplifying
27a2b2 + 42ab + 8 = 0

Reorder the terms:
8 + 42ab + 27a2b2 = 0

Solving
8 + 42ab + 27a2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + 3ab)(2 + 9ab) = 0

Subproblem 1
Set the factor '(4 + 3ab)' equal to zero and attempt to solve:

Simplifying
4 + 3ab = 0

Solving
4 + 3ab = 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 + 3ab = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3ab = 0 + -4
3ab = 0 + -4

Combine like terms: 0 + -4 = -4
3ab = -4

Divide each side by '3b'.
a = -1.333333333b-1

Simplifying
a = -1.333333333b-1
Subproblem 2
Set the factor '(2 + 9ab)' equal to zero and attempt to solve:

Simplifying
2 + 9ab = 0

Solving
2 + 9ab = 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 + 9ab = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9ab = 0 + -2
9ab = 0 + -2

Combine like terms: 0 + -2 = -2
9ab = -2

Divide each side by '9b'.
a = -0.2222222222b-1

Simplifying
a = -0.2222222222b-1
Solution
a = {-1.333333333b-1, -0.2222222222b-1}