2x^2y+8xy-58y=0

Solution for 2x^2y+8xy-58y=0 equation:

Simplifying
2x2y + 8xy + -58y = 0

Reorder the terms:
8xy + 2x2y + -58y = 0

Solving
8xy + 2x2y + -58y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(4x + x2 + -29) = 0

Ignore the factor 2.
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 '(4x + x2 + -29)' equal to zero and attempt to solve:

Simplifying
4x + x2 + -29 = 0

Reorder the terms:
-29 + 4x + x2 = 0

Solving
-29 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 4x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 4x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 4x + x2 = 0 + 29
4x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
4x + x2 = 29

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 29 + 4

Reorder the terms:
4 + 4x + x2 = 29 + 4

Combine like terms: 29 + 4 = 33
4 + 4x + x2 = 33

Factor a perfect square on the left side:
(x + 2)(x + 2) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + 2) equal to 5.744562647 and -5.744562647.

Subproblem 1
x + 2 = 5.744562647

Simplifying
x + 2 = 5.744562647

Reorder the terms:
2 + x = 5.744562647

Solving
2 + x = 5.744562647

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 5.744562647 + -2

Combine like terms: 2 + -2 = 0
0 + x = 5.744562647 + -2
x = 5.744562647 + -2

Combine like terms: 5.744562647 + -2 = 3.744562647
x = 3.744562647

Simplifying
x = 3.744562647

Subproblem 2
x + 2 = -5.744562647

Simplifying
x + 2 = -5.744562647

Reorder the terms:
2 + x = -5.744562647

Solving
2 + x = -5.744562647

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -5.744562647 + -2

Combine like terms: 2 + -2 = 0
0 + x = -5.744562647 + -2
x = -5.744562647 + -2

Combine like terms: -5.744562647 + -2 = -7.744562647
x = -7.744562647

Simplifying
x = -7.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.744562647, -7.744562647}
Solution
x = {3.744562647, -7.744562647}