3x^2y+12xy-57y=

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Solution for 3x^2y+12xy-57y= equation: 


Simplifying
3x2y + 12xy + -57y = 0

Reorder the terms:
12xy + 3x2y + -57y = 0

Solving
12xy + 3x2y + -57y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(4x + x2 + -19) = 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 '(4x + x2 + -19)' equal to zero and attempt to solve:

Simplifying
4x + x2 + -19 = 0

Reorder the terms:
-19 + 4x + x2 = 0

Solving
-19 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 4x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 4x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 4x + x2 = 0 + 19
4x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
4x + x2 = 19

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 = 19 + 4

Reorder the terms:
4 + 4x + x2 = 19 + 4

Combine like terms: 19 + 4 = 23
4 + 4x + x2 = 23

Factor a perfect square on the left side:
(x + 2)(x + 2) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + 2) equal to 4.795831523 and -4.795831523.


Subproblem 1
x + 2 = 4.795831523

Simplifying
x + 2 = 4.795831523

Reorder the terms:
2 + x = 4.795831523

Solving
2 + x = 4.795831523

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 = 4.795831523 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.795831523 + -2
x = 4.795831523 + -2

Combine like terms: 4.795831523 + -2 = 2.795831523
x = 2.795831523

Simplifying
x = 2.795831523


Subproblem 2
x + 2 = -4.795831523

Simplifying
x + 2 = -4.795831523

Reorder the terms:
2 + x = -4.795831523

Solving
2 + x = -4.795831523

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 = -4.795831523 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.795831523 + -2
x = -4.795831523 + -2

Combine like terms: -4.795831523 + -2 = -6.795831523
x = -6.795831523

Simplifying
x = -6.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.795831523, -6.795831523}
Solution
x = {2.795831523, -6.795831523}

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