x(x)(y)(y)+4xy+3=0

Solution for x(x)(y)(y)+4xy+3=0 equation:

Simplifying
x(x)(y)(y) + 4xy + 3 = 0

Multiply x * x
x2 * y * y + 4xy + 3 = 0

Multiply x2 * y
x2y * y + 4xy + 3 = 0

Multiply x2y * y
x2y2 + 4xy + 3 = 0

Reorder the terms:
3 + 4xy + x2y2 = 0

Solving
3 + 4xy + x2y2 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + xy = 0

Solving
3 + xy = 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 + xy = 0 + -3

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

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

Divide each side by 'y'.
x = -3y-1

Simplifying
x = -3y-1
Subproblem 2
Set the factor '(1 + xy)' equal to zero and attempt to solve:

Simplifying
1 + xy = 0

Solving
1 + xy = 0

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

Add '-1' to each side of the equation.
1 + -1 + xy = 0 + -1

Combine like terms: 1 + -1 = 0
0 + xy = 0 + -1
xy = 0 + -1

Combine like terms: 0 + -1 = -1
xy = -1

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

Simplifying
x = -1y-1
Solution
x = {-3y-1, -1y-1}