5n^2(5n^2-2n+4)=

Solution for 5n^2(5n^2-2n+4)= equation:

Simplifying
5n2(5n2 + -2n + 4) = 0

Reorder the terms:
5n2(4 + -2n + 5n2) = 0
(4 * 5n2 + -2n * 5n2 + 5n2 * 5n2) = 0
(20n2 + -10n3 + 25n4) = 0

Solving
20n2 + -10n3 + 25n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5n2'.
5n2(4 + -2n + 5n2) = 0

Ignore the factor 5.
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 + 5n2)' equal to zero and attempt to solve:

Simplifying
4 + -2n + 5n2 = 0

Solving
4 + -2n + 5n2 = 0

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

Divide each side by '5'.
0.8 + -0.4n + n2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -0.4n + -0.8 + n2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -0.4n + n2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -0.4n + n2 = 0 + -0.8
-0.4n + n2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-0.4n + n2 = -0.8

The n term is -0.4n.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4n + 0.04 + n2 = -0.8 + 0.04

Reorder the terms:
0.04 + -0.4n + n2 = -0.8 + 0.04

Combine like terms: -0.8 + 0.04 = -0.76
0.04 + -0.4n + n2 = -0.76

Factor a perfect square on the left side:
(n + -0.2)(n + -0.2) = -0.76

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}