4n^4+56n^3+192n^2=0

Solution for 4n^4+56n^3+192n^2=0 equation:

Simplifying
4n4 + 56n3 + 192n2 = 0

Reorder the terms:
192n2 + 56n3 + 4n4 = 0

Solving
192n2 + 56n3 + 4n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4n2'.
4n2(48 + 14n + n2) = 0

Factor a trinomial.
4n2((8 + n)(6 + n)) = 0

Ignore the factor 4.
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 '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 3
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Solution
n = {0, -8, -6}