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

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

Simplifying
2n(n2 + 3n + 4) = 0

Reorder the terms:
2n(4 + 3n + n2) = 0
(4 * 2n + 3n * 2n + n2 * 2n) = 0
(8n + 6n2 + 2n3) = 0

Solving
8n + 6n2 + 2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(4 + 3n + n2) = 0

Ignore the factor 2.
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 '(4 + 3n + n2)' equal to zero and attempt to solve:

Simplifying
4 + 3n + n2 = 0

Solving
4 + 3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 3n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + 3n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n + n2 = 0 + -4
3n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
3n + n2 = -4

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = -4 + 2.25

Reorder the terms:
2.25 + 3n + n2 = -4 + 2.25

Combine like terms: -4 + 2.25 = -1.75
2.25 + 3n + n2 = -1.75

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = -1.75

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}