3x^2y+12xy-6y=0

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Solution for 3x^2y+12xy-6y=0 equation: 


Simplifying
3x2y + 12xy + -6y = 0

Reorder the terms:
12xy + 3x2y + -6y = 0

Solving
12xy + 3x2y + -6y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(4x + x2 + -2) = 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 + -2)' equal to zero and attempt to solve:

Simplifying
4x + x2 + -2 = 0

Reorder the terms:
-2 + 4x + x2 = 0

Solving
-2 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 4x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4x + x2 = 0 + 2
4x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
4x + x2 = 2

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 = 2 + 4

Reorder the terms:
4 + 4x + x2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4x + x2 = 6

Factor a perfect square on the left side:
(x + 2)(x + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 2) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 2 = 2.449489743

Simplifying
x + 2 = 2.449489743

Reorder the terms:
2 + x = 2.449489743

Solving
2 + x = 2.449489743

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 = 2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.449489743 + -2
x = 2.449489743 + -2

Combine like terms: 2.449489743 + -2 = 0.449489743
x = 0.449489743

Simplifying
x = 0.449489743


Subproblem 2
x + 2 = -2.449489743

Simplifying
x + 2 = -2.449489743

Reorder the terms:
2 + x = -2.449489743

Solving
2 + x = -2.449489743

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 = -2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.449489743 + -2
x = -2.449489743 + -2

Combine like terms: -2.449489743 + -2 = -4.449489743
x = -4.449489743

Simplifying
x = -4.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.449489743, -4.449489743}
Solution
x = {0.449489743, -4.449489743}

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