6x^2y+72xy-42y=0

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Solution for 6x^2y+72xy-42y=0 equation: 


Simplifying
6x2y + 72xy + -42y = 0

Reorder the terms:
72xy + 6x2y + -42y = 0

Solving
72xy + 6x2y + -42y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6y'.
6y(12x + x2 + -7) = 0

Ignore the factor 6.

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 '(12x + x2 + -7)' equal to zero and attempt to solve:

Simplifying
12x + x2 + -7 = 0

Reorder the terms:
-7 + 12x + x2 = 0

Solving
-7 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 12x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 12x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 12x + x2 = 0 + 7
12x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
12x + x2 = 7

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 7 + 36

Reorder the terms:
36 + 12x + x2 = 7 + 36

Combine like terms: 7 + 36 = 43
36 + 12x + x2 = 43

Factor a perfect square on the left side:
(x + 6)(x + 6) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + 6) equal to 6.557438524 and -6.557438524.


Subproblem 1
x + 6 = 6.557438524

Simplifying
x + 6 = 6.557438524

Reorder the terms:
6 + x = 6.557438524

Solving
6 + x = 6.557438524

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 6.557438524 + -6

Combine like terms: 6 + -6 = 0
0 + x = 6.557438524 + -6
x = 6.557438524 + -6

Combine like terms: 6.557438524 + -6 = 0.557438524
x = 0.557438524

Simplifying
x = 0.557438524


Subproblem 2
x + 6 = -6.557438524

Simplifying
x + 6 = -6.557438524

Reorder the terms:
6 + x = -6.557438524

Solving
6 + x = -6.557438524

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -6.557438524 + -6

Combine like terms: 6 + -6 = 0
0 + x = -6.557438524 + -6
x = -6.557438524 + -6

Combine like terms: -6.557438524 + -6 = -12.557438524
x = -12.557438524

Simplifying
x = -12.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.557438524, -12.557438524}
Solution
x = {0.557438524, -12.557438524}

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