2(x+y)+6n(x+y)=0

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Solution for 2(x+y)+6n(x+y)=0 equation: 


Simplifying
2(x + y) + 6n(x + y) = 0
(x * 2 + y * 2) + 6n(x + y) = 0
(2x + 2y) + 6n(x + y) = 0
2x + 2y + (x * 6n + y * 6n) = 0
2x + 2y + (6nx + 6ny) = 0

Reorder the terms:
6nx + 6ny + 2x + 2y = 0

Solving
6nx + 6ny + 2x + 2y = 0

Solving for variable 'n'.

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

Add '-2x' to each side of the equation.
6nx + 6ny + 2x + -2x + 2y = 0 + -2x

Combine like terms: 2x + -2x = 0
6nx + 6ny + 0 + 2y = 0 + -2x
6nx + 6ny + 2y = 0 + -2x
Remove the zero:
6nx + 6ny + 2y = -2x

Add '-2y' to each side of the equation.
6nx + 6ny + 2y + -2y = -2x + -2y

Combine like terms: 2y + -2y = 0
6nx + 6ny + 0 = -2x + -2y
6nx + 6ny = -2x + -2y

Reorder the terms:
6nx + 6ny + 2x + 2y = -2x + 2x + -2y + 2y

Combine like terms: -2x + 2x = 0
6nx + 6ny + 2x + 2y = 0 + -2y + 2y
6nx + 6ny + 2x + 2y = -2y + 2y

Combine like terms: -2y + 2y = 0
6nx + 6ny + 2x + 2y = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3nx + 3ny + x + y) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3nx + 3ny + x + y)' equal to zero and attempt to solve:

Simplifying
3nx + 3ny + x + y = 0

Solving
3nx + 3ny + x + y = 0

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

Add '-1x' to each side of the equation.
3nx + 3ny + x + -1x + y = 0 + -1x

Combine like terms: x + -1x = 0
3nx + 3ny + 0 + y = 0 + -1x
3nx + 3ny + y = 0 + -1x
Remove the zero:
3nx + 3ny + y = -1x

Add '-1y' to each side of the equation.
3nx + 3ny + y + -1y = -1x + -1y

Combine like terms: y + -1y = 0
3nx + 3ny + 0 = -1x + -1y
3nx + 3ny = -1x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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