3x^2y+45xy-87y=0

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Solution for 3x^2y+45xy-87y=0 equation: 


Simplifying
3x2y + 45xy + -87y = 0

Reorder the terms:
45xy + 3x2y + -87y = 0

Solving
45xy + 3x2y + -87y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(15x + x2 + -29) = 0

Ignore the factor 3.

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 '(15x + x2 + -29)' equal to zero and attempt to solve:

Simplifying
15x + x2 + -29 = 0

Reorder the terms:
-29 + 15x + x2 = 0

Solving
-29 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 15x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 15x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 15x + x2 = 0 + 29
15x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
15x + x2 = 29

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 29 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 29 + 56.25

Combine like terms: 29 + 56.25 = 85.25
56.25 + 15x + x2 = 85.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x + 7.5) equal to 9.233092656 and -9.233092656.


Subproblem 1
x + 7.5 = 9.233092656

Simplifying
x + 7.5 = 9.233092656

Reorder the terms:
7.5 + x = 9.233092656

Solving
7.5 + x = 9.233092656

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 9.233092656 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 9.233092656 + -7.5
x = 9.233092656 + -7.5

Combine like terms: 9.233092656 + -7.5 = 1.733092656
x = 1.733092656

Simplifying
x = 1.733092656


Subproblem 2
x + 7.5 = -9.233092656

Simplifying
x + 7.5 = -9.233092656

Reorder the terms:
7.5 + x = -9.233092656

Solving
7.5 + x = -9.233092656

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -9.233092656 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -9.233092656 + -7.5
x = -9.233092656 + -7.5

Combine like terms: -9.233092656 + -7.5 = -16.733092656
x = -16.733092656

Simplifying
x = -16.733092656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.733092656, -16.733092656}
Solution
x = {1.733092656, -16.733092656}

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