16x^2y^2+42xy+27=0

Solution for 16x^2y^2+42xy+27=0 equation:

Simplifying
16x2y2 + 42xy + 27 = 0

Reorder the terms:
27 + 42xy + 16x2y2 = 0

Solving
27 + 42xy + 16x2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 2xy)(9 + 8xy) = 0

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

Simplifying
3 + 2xy = 0

Solving
3 + 2xy = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2xy = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2xy = 0 + -3
2xy = 0 + -3

Combine like terms: 0 + -3 = -3
2xy = -3

Divide each side by '2y'.
x = -1.5y-1

Simplifying
x = -1.5y-1
Subproblem 2
Set the factor '(9 + 8xy)' equal to zero and attempt to solve:

Simplifying
9 + 8xy = 0

Solving
9 + 8xy = 0

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

Add '-9' to each side of the equation.
9 + -9 + 8xy = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8xy = 0 + -9
8xy = 0 + -9

Combine like terms: 0 + -9 = -9
8xy = -9

Divide each side by '8y'.
x = -1.125y-1

Simplifying
x = -1.125y-1
Solution
x = {-1.5y-1, -1.125y-1}