(x^3n+2y^2n)(x^3n+2y^2n)=0

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Solution for (x^3n+2y^2n)(x^3n+2y^2n)=0 equation: 


Simplifying
(x3n + 2y2n)(x3n + 2y2n) = 0

Multiply (nx3 + 2ny2) * (nx3 + 2ny2)
(nx3(nx3 + 2ny2) + 2ny2 * (nx3 + 2ny2)) = 0
((nx3 * nx3 + 2ny2 * nx3) + 2ny2 * (nx3 + 2ny2)) = 0

Reorder the terms:
((2n2x3y2 + n2x6) + 2ny2 * (nx3 + 2ny2)) = 0
((2n2x3y2 + n2x6) + 2ny2 * (nx3 + 2ny2)) = 0
(2n2x3y2 + n2x6 + (nx3 * 2ny2 + 2ny2 * 2ny2)) = 0
(2n2x3y2 + n2x6 + (2n2x3y2 + 4n2y4)) = 0

Reorder the terms:
(2n2x3y2 + 2n2x3y2 + n2x6 + 4n2y4) = 0

Combine like terms: 2n2x3y2 + 2n2x3y2 = 4n2x3y2
(4n2x3y2 + n2x6 + 4n2y4) = 0

Solving
4n2x3y2 + n2x6 + 4n2y4 = 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), 'n2'.
n2(4x3y2 + x6 + 4y4) = 0

Factor a trinomial.
n2((x3 + 2y2)(x3 + 2y2)) = 0


Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}

Subproblem 2
Set the factor '(x3 + 2y2)' equal to zero and attempt to solve:

Simplifying
x3 + 2y2 = 0

Solving
x3 + 2y2 = 0

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

Add '-1x3' to each side of the equation.
x3 + -1x3 + 2y2 = 0 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 2y2 = 0 + -1x3
2y2 = 0 + -1x3
Remove the zero:
2y2 = -1x3

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x3 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x3 + -2y2

Simplifying
0 = -1x3 + -2y2

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 '(x3 + 2y2)' equal to zero and attempt to solve:

Simplifying
x3 + 2y2 = 0

Solving
x3 + 2y2 = 0

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

Add '-1x3' to each side of the equation.
x3 + -1x3 + 2y2 = 0 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 2y2 = 0 + -1x3
2y2 = 0 + -1x3
Remove the zero:
2y2 = -1x3

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -1x3 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -1x3 + -2y2

Simplifying
0 = -1x3 + -2y2

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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