10x^2n+47xny+42y^2n=0

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Solution for 10x^2n+47xny+42y^2n=0 equation: 


Simplifying
10x2n + 47xny + 42y2n = 0

Reorder the terms:
47nxy + 10nx2 + 42ny2 = 0

Solving
47nxy + 10nx2 + 42ny2 = 0

Solving for variable 'n'.

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(47xy + 10x2 + 42y2) = 0

Factor a trinomial.
n((5x + 6y)(2x + 7y)) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(5x + 6y)' equal to zero and attempt to solve:

Simplifying
5x + 6y = 0

Solving
5x + 6y = 0

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

Add '-5x' to each side of the equation.
5x + -5x + 6y = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 6y = 0 + -5x
6y = 0 + -5x
Remove the zero:
6y = -5x

Add '-6y' to each side of the equation.
6y + -6y = -5x + -6y

Combine like terms: 6y + -6y = 0
0 = -5x + -6y

Simplifying
0 = -5x + -6y

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(2x + 7y)' equal to zero and attempt to solve:

Simplifying
2x + 7y = 0

Solving
2x + 7y = 0

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

Add '-2x' to each side of the equation.
2x + -2x + 7y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 7y = 0 + -2x
7y = 0 + -2x
Remove the zero:
7y = -2x

Add '-7y' to each side of the equation.
7y + -7y = -2x + -7y

Combine like terms: 7y + -7y = 0
0 = -2x + -7y

Simplifying
0 = -2x + -7y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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