n^2(-2n^2+4n-8)=

Solution for n^2(-2n^2+4n-8)= equation:

Simplifying
n2(-2n2 + 4n + -8) = 0

Reorder the terms:
n2(-8 + 4n + -2n2) = 0
(-8 * n2 + 4n * n2 + -2n2 * n2) = 0
(-8n2 + 4n3 + -2n4) = 0

Solving
-8n2 + 4n3 + -2n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n2'.
2n2(-4 + 2n + -1n2) = 0

Ignore the factor 2.
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 '(-4 + 2n + -1n2)' equal to zero and attempt to solve:

Simplifying
-4 + 2n + -1n2 = 0

Solving
-4 + 2n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -2n + n2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + -2n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2n + n2 = 0 + -4
-2n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2n + n2 = -4

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = -4 + 1

Reorder the terms:
1 + -2n + n2 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + -2n + n2 = -3

Factor a perfect square on the left side:
(n + -1)(n + -1) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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