32x^2y+45xy-87y=0

Solution for 32x^2y+45xy-87y=0 equation:

Simplifying
32x2y + 45xy + -87y = 0

Reorder the terms:
45xy + 32x2y + -87y = 0

Solving
45xy + 32x2y + -87y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(45x + 32x2 + -87) = 0

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 '(45x + 32x2 + -87)' equal to zero and attempt to solve:

Simplifying
45x + 32x2 + -87 = 0

Reorder the terms:
-87 + 45x + 32x2 = 0

Solving
-87 + 45x + 32x2 = 0

Begin completing the square.  Divide all terms by
32 the coefficient of the squared term: 

Divide each side by '32'.
-2.71875 + 1.40625x + x2 = 0

Move the constant term to the right:

Add '2.71875' to each side of the equation.
-2.71875 + 1.40625x + 2.71875 + x2 = 0 + 2.71875

Reorder the terms:
-2.71875 + 2.71875 + 1.40625x + x2 = 0 + 2.71875

Combine like terms: -2.71875 + 2.71875 = 0.00000
0.00000 + 1.40625x + x2 = 0 + 2.71875
1.40625x + x2 = 0 + 2.71875

Combine like terms: 0 + 2.71875 = 2.71875
1.40625x + x2 = 2.71875

The x term is 1.40625x.  Take half its coefficient (0.703125).
Square it (0.4943847656) and add it to both sides.

Add '0.4943847656' to each side of the equation.
1.40625x + 0.4943847656 + x2 = 2.71875 + 0.4943847656

Reorder the terms:
0.4943847656 + 1.40625x + x2 = 2.71875 + 0.4943847656

Combine like terms: 2.71875 + 0.4943847656 = 3.2131347656
0.4943847656 + 1.40625x + x2 = 3.2131347656

Factor a perfect square on the left side:
(x + 0.703125)(x + 0.703125) = 3.2131347656

Calculate the square root of the right side: 1.792521901

Break this problem into two subproblems by setting 
(x + 0.703125) equal to 1.792521901 and -1.792521901.

Subproblem 1
x + 0.703125 = 1.792521901

Simplifying
x + 0.703125 = 1.792521901

Reorder the terms:
0.703125 + x = 1.792521901

Solving
0.703125 + x = 1.792521901

Solving for variable 'x'.

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

Add '-0.703125' to each side of the equation.
0.703125 + -0.703125 + x = 1.792521901 + -0.703125

Combine like terms: 0.703125 + -0.703125 = 0.000000
0.000000 + x = 1.792521901 + -0.703125
x = 1.792521901 + -0.703125

Combine like terms: 1.792521901 + -0.703125 = 1.089396901
x = 1.089396901

Simplifying
x = 1.089396901

Subproblem 2
x + 0.703125 = -1.792521901

Simplifying
x + 0.703125 = -1.792521901

Reorder the terms:
0.703125 + x = -1.792521901

Solving
0.703125 + x = -1.792521901

Solving for variable 'x'.

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

Add '-0.703125' to each side of the equation.
0.703125 + -0.703125 + x = -1.792521901 + -0.703125

Combine like terms: 0.703125 + -0.703125 = 0.000000
0.000000 + x = -1.792521901 + -0.703125
x = -1.792521901 + -0.703125

Combine like terms: -1.792521901 + -0.703125 = -2.495646901
x = -2.495646901

Simplifying
x = -2.495646901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.089396901, -2.495646901}
Solution
x = {1.089396901, -2.495646901}