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

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

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

Reorder the terms:
2n(5 + n)(2n + 4) = 0

Reorder the terms:
2n(5 + n)(4 + 2n) = 0

Multiply (5 + n) * (4 + 2n)
2n(5(4 + 2n) + n(4 + 2n)) = 0
2n((4 * 5 + 2n * 5) + n(4 + 2n)) = 0
2n((20 + 10n) + n(4 + 2n)) = 0
2n(20 + 10n + (4 * n + 2n * n)) = 0
2n(20 + 10n + (4n + 2n2)) = 0

Combine like terms: 10n + 4n = 14n
2n(20 + 14n + 2n2) = 0
(20 * 2n + 14n * 2n + 2n2 * 2n) = 0
(40n + 28n2 + 4n3) = 0

Solving
40n + 28n2 + 4n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4n'.
4n(10 + 7n + n2) = 0

Factor a trinomial.
4n((5 + n)(2 + n)) = 0

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

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Subproblem 3
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

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

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

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

Simplifying
n = -2
Solution
n = {0, -5, -2}