(n^3-4n^2)(-n+4)=0

Solution for (n^3-4n^2)(-n+4)=0 equation:

Simplifying
(n3 + -4n2)(-1n + 4) = 0

Reorder the terms:
(-4n2 + n3)(-1n + 4) = 0

Reorder the terms:
(-4n2 + n3)(4 + -1n) = 0

Multiply (-4n2 + n3) * (4 + -1n)
(-4n2 * (4 + -1n) + n3(4 + -1n)) = 0
((4 * -4n2 + -1n * -4n2) + n3(4 + -1n)) = 0
((-16n2 + 4n3) + n3(4 + -1n)) = 0
(-16n2 + 4n3 + (4 * n3 + -1n * n3)) = 0
(-16n2 + 4n3 + (4n3 + -1n4)) = 0

Combine like terms: 4n3 + 4n3 = 8n3
(-16n2 + 8n3 + -1n4) = 0

Solving
-16n2 + 8n3 + -1n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(-16 + 8n + -1n2) = 0

Factor a trinomial.
n2((-4 + n)(4 + -1n)) = 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 '(-4 + n)' equal to zero and attempt to solve:

Simplifying
-4 + n = 0

Solving
-4 + n = 0

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

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

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

Combine like terms: 0 + 4 = 4
n = 4

Simplifying
n = 4
Subproblem 3
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {0, 4, 4}