n^2[n+1][2n^3+4n^2+n-1][n+6]=0

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Solution for n^2[n+1][2n^3+4n^2+n-1][n+6]=0 equation: 


Simplifying
n2[n + 1][2n3 + 4n2 + n + -1][n + 6] = 0

Reorder the terms:
n2[1 + n][2n3 + 4n2 + n + -1][n + 6] = 0

Reorder the terms:
n2[1 + n][-1 + n + 4n2 + 2n3][n + 6] = 0

Reorder the terms:
n2[1 + n][-1 + n + 4n2 + 2n3][6 + n] = 0

Multiply [1 + n] * [-1 + n + 4n2 + 2n3]
n2[1[-1 + n + 4n2 + 2n3] + n[-1 + n + 4n2 + 2n3]][6 + n] = 0
n2[[-1 * 1 + n * 1 + 4n2 * 1 + 2n3 * 1] + n[-1 + n + 4n2 + 2n3]][6 + n] = 0
n2[[-1 + 1n + 4n2 + 2n3] + n[-1 + n + 4n2 + 2n3]][6 + n] = 0
n2[-1 + 1n + 4n2 + 2n3 + [-1 * n + n * n + 4n2 * n + 2n3 * n]][6 + n] = 0
n2[-1 + 1n + 4n2 + 2n3 + [-1n + n2 + 4n3 + 2n4]][6 + n] = 0

Reorder the terms:
n2[-1 + 1n + -1n + 4n2 + n2 + 2n3 + 4n3 + 2n4][6 + n] = 0

Combine like terms: 1n + -1n = 0
n2[-1 + 0 + 4n2 + n2 + 2n3 + 4n3 + 2n4][6 + n] = 0
n2[-1 + 4n2 + n2 + 2n3 + 4n3 + 2n4][6 + n] = 0

Combine like terms: 4n2 + n2 = 5n2
n2[-1 + 5n2 + 2n3 + 4n3 + 2n4][6 + n] = 0

Combine like terms: 2n3 + 4n3 = 6n3
n2[-1 + 5n2 + 6n3 + 2n4][6 + n] = 0

Multiply [-1 + 5n2 + 6n3 + 2n4] * [6 + n]
n2[-1[6 + n] + 5n2 * [6 + n] + 6n3 * [6 + n] + 2n4 * [6 + n]] = 0
n2[[6 * -1 + n * -1] + 5n2 * [6 + n] + 6n3 * [6 + n] + 2n4 * [6 + n]] = 0
n2[[-6 + -1n] + 5n2 * [6 + n] + 6n3 * [6 + n] + 2n4 * [6 + n]] = 0
n2[-6 + -1n + [6 * 5n2 + n * 5n2] + 6n3 * [6 + n] + 2n4 * [6 + n]] = 0
n2[-6 + -1n + [30n2 + 5n3] + 6n3 * [6 + n] + 2n4 * [6 + n]] = 0
n2[-6 + -1n + 30n2 + 5n3 + [6 * 6n3 + n * 6n3] + 2n4 * [6 + n]] = 0
n2[-6 + -1n + 30n2 + 5n3 + [36n3 + 6n4] + 2n4 * [6 + n]] = 0
n2[-6 + -1n + 30n2 + 5n3 + 36n3 + 6n4 + [6 * 2n4 + n * 2n4]] = 0
n2[-6 + -1n + 30n2 + 5n3 + 36n3 + 6n4 + [12n4 + 2n5]] = 0

Combine like terms: 5n3 + 36n3 = 41n3
n2[-6 + -1n + 30n2 + 41n3 + 6n4 + 12n4 + 2n5] = 0

Combine like terms: 6n4 + 12n4 = 18n4
n2[-6 + -1n + 30n2 + 41n3 + 18n4 + 2n5] = 0
[-6 * n2 + -1n * n2 + 30n2 * n2 + 41n3 * n2 + 18n4 * n2 + 2n5 * n2] = 0
[-6n2 + -1n3 + 30n4 + 41n5 + 18n6 + 2n7] = 0

Solving
-6n2 + -1n3 + 30n4 + 41n5 + 18n6 + 2n7 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(-6 + -1n + 30n2 + 41n3 + 18n4 + 2n5) = 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 '(-6 + -1n + 30n2 + 41n3 + 18n4 + 2n5)' equal to zero and attempt to solve:

Simplifying
-6 + -1n + 30n2 + 41n3 + 18n4 + 2n5 = 0

Solving
-6 + -1n + 30n2 + 41n3 + 18n4 + 2n5 = 0

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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