3nx^8-6nx^4-45n=0

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Solution for 3nx^8-6nx^4-45n=0 equation: 


Simplifying
3nx8 + -6nx4 + -45n = 0

Reorder the terms:
-45n + -6nx4 + 3nx8 = 0

Solving
-45n + -6nx4 + 3nx8 = 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), '3n'.
3n(-15 + -2x4 + x8) = 0

Factor a trinomial.
3n((-3 + -1x4)(5 + -1x4)) = 0

Ignore the factor 3.

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 '(-3 + -1x4)' equal to zero and attempt to solve:

Simplifying
-3 + -1x4 = 0

Solving
-3 + -1x4 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x4 = 0 + 3
-1x4 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x4 = 3

Add 'x4' to each side of the equation.
-1x4 + x4 = 3 + x4

Combine like terms: -1x4 + x4 = 0
0 = 3 + x4

Simplifying
0 = 3 + x4

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 '(5 + -1x4)' equal to zero and attempt to solve:

Simplifying
5 + -1x4 = 0

Solving
5 + -1x4 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x4 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x4 = 0 + -5
-1x4 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x4 = -5

Add 'x4' to each side of the equation.
-1x4 + x4 = -5 + x4

Combine like terms: -1x4 + x4 = 0
0 = -5 + x4

Simplifying
0 = -5 + x4

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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