3x^2y+27xy-87y=0

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Solution for 3x^2y+27xy-87y=0 equation: 


Simplifying
3x2y + 27xy + -87y = 0

Reorder the terms:
27xy + 3x2y + -87y = 0

Solving
27xy + 3x2y + -87y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(9x + 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 '(9x + x2 + -29)' equal to zero and attempt to solve:

Simplifying
9x + x2 + -29 = 0

Reorder the terms:
-29 + 9x + x2 = 0

Solving
-29 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 9x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 9x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 9x + x2 = 0 + 29
9x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
9x + x2 = 29

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 29 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 29 + 20.25

Combine like terms: 29 + 20.25 = 49.25
20.25 + 9x + x2 = 49.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(x + 4.5) equal to 7.017834424 and -7.017834424.


Subproblem 1
x + 4.5 = 7.017834424

Simplifying
x + 4.5 = 7.017834424

Reorder the terms:
4.5 + x = 7.017834424

Solving
4.5 + x = 7.017834424

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 7.017834424 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 7.017834424 + -4.5
x = 7.017834424 + -4.5

Combine like terms: 7.017834424 + -4.5 = 2.517834424
x = 2.517834424

Simplifying
x = 2.517834424


Subproblem 2
x + 4.5 = -7.017834424

Simplifying
x + 4.5 = -7.017834424

Reorder the terms:
4.5 + x = -7.017834424

Solving
4.5 + x = -7.017834424

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -7.017834424 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -7.017834424 + -4.5
x = -7.017834424 + -4.5

Combine like terms: -7.017834424 + -4.5 = -11.517834424
x = -11.517834424

Simplifying
x = -11.517834424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.517834424, -11.517834424}
Solution
x = {2.517834424, -11.517834424}

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