4x^2y+48xy-76y=0

Solution for 4x^2y+48xy-76y=0 equation:

Simplifying
4x2y + 48xy + -76y = 0

Reorder the terms:
48xy + 4x2y + -76y = 0

Solving
48xy + 4x2y + -76y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(12x + x2 + -19) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

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 '(12x + x2 + -19)' equal to zero and attempt to solve:

Simplifying
12x + x2 + -19 = 0

Reorder the terms:
-19 + 12x + x2 = 0

Solving
-19 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 12x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 12x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 12x + x2 = 0 + 19
12x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
12x + x2 = 19

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 19 + 36

Reorder the terms:
36 + 12x + x2 = 19 + 36

Combine like terms: 19 + 36 = 55
36 + 12x + x2 = 55

Factor a perfect square on the left side:
(x + 6)(x + 6) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 6) equal to 7.416198487 and -7.416198487.

Subproblem 1
x + 6 = 7.416198487

Simplifying
x + 6 = 7.416198487

Reorder the terms:
6 + x = 7.416198487

Solving
6 + x = 7.416198487

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 7.416198487 + -6

Combine like terms: 6 + -6 = 0
0 + x = 7.416198487 + -6
x = 7.416198487 + -6

Combine like terms: 7.416198487 + -6 = 1.416198487
x = 1.416198487

Simplifying
x = 1.416198487

Subproblem 2
x + 6 = -7.416198487

Simplifying
x + 6 = -7.416198487

Reorder the terms:
6 + x = -7.416198487

Solving
6 + x = -7.416198487

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -7.416198487 + -6

Combine like terms: 6 + -6 = 0
0 + x = -7.416198487 + -6
x = -7.416198487 + -6

Combine like terms: -7.416198487 + -6 = -13.416198487
x = -13.416198487

Simplifying
x = -13.416198487

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.416198487, -13.416198487}
Solution
x = {1.416198487, -13.416198487}