(3y-nx)(2y-nx)=0

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Solution for (3y-nx)(2y-nx)=0 equation: 


Simplifying
(3y + -1nx)(2y + -1nx) = 0

Reorder the terms:
(-1nx + 3y)(2y + -1nx) = 0

Reorder the terms:
(-1nx + 3y)(-1nx + 2y) = 0

Multiply (-1nx + 3y) * (-1nx + 2y)
(-1nx * (-1nx + 2y) + 3y * (-1nx + 2y)) = 0
((-1nx * -1nx + 2y * -1nx) + 3y * (-1nx + 2y)) = 0

Reorder the terms:
((-2nxy + 1n2x2) + 3y * (-1nx + 2y)) = 0
((-2nxy + 1n2x2) + 3y * (-1nx + 2y)) = 0
(-2nxy + 1n2x2 + (-1nx * 3y + 2y * 3y)) = 0
(-2nxy + 1n2x2 + (-3nxy + 6y2)) = 0

Reorder the terms:
(-2nxy + -3nxy + 1n2x2 + 6y2) = 0

Combine like terms: -2nxy + -3nxy = -5nxy
(-5nxy + 1n2x2 + 6y2) = 0

Solving
-5nxy + 1n2x2 + 6y2 = 0

Solving for variable 'n'.

Factor a trinomial.
(nx + -3y)(nx + -2y) = 0


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

Simplifying
nx + -3y = 0

Solving
nx + -3y = 0

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

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

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

Divide each side by 'x'.
n = 3x-1y

Simplifying
n = 3x-1y

Subproblem 2
Set the factor '(nx + -2y)' equal to zero and attempt to solve:

Simplifying
nx + -2y = 0

Solving
nx + -2y = 0

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

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

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

Divide each side by 'x'.
n = 2x-1y

Simplifying
n = 2x-1y
Solution
n = {3x-1y, 2x-1y}

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