3x^2y+42xy-33y=0

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Solution for 3x^2y+42xy-33y=0 equation: 


Simplifying
3x2y + 42xy + -33y = 0

Reorder the terms:
42xy + 3x2y + -33y = 0

Solving
42xy + 3x2y + -33y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(14x + x2 + -11) = 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 '(14x + x2 + -11)' equal to zero and attempt to solve:

Simplifying
14x + x2 + -11 = 0

Reorder the terms:
-11 + 14x + x2 = 0

Solving
-11 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 14x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 14x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 14x + x2 = 0 + 11
14x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
14x + x2 = 11

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 11 + 49

Reorder the terms:
49 + 14x + x2 = 11 + 49

Combine like terms: 11 + 49 = 60
49 + 14x + x2 = 60

Factor a perfect square on the left side:
(x + 7)(x + 7) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + 7) equal to 7.745966692 and -7.745966692.


Subproblem 1
x + 7 = 7.745966692

Simplifying
x + 7 = 7.745966692

Reorder the terms:
7 + x = 7.745966692

Solving
7 + x = 7.745966692

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 7.745966692 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.745966692 + -7
x = 7.745966692 + -7

Combine like terms: 7.745966692 + -7 = 0.745966692
x = 0.745966692

Simplifying
x = 0.745966692


Subproblem 2
x + 7 = -7.745966692

Simplifying
x + 7 = -7.745966692

Reorder the terms:
7 + x = -7.745966692

Solving
7 + x = -7.745966692

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -7.745966692 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.745966692 + -7
x = -7.745966692 + -7

Combine like terms: -7.745966692 + -7 = -14.745966692
x = -14.745966692

Simplifying
x = -14.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.745966692, -14.745966692}
Solution
x = {0.745966692, -14.745966692}

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