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

Solution for 2n(n-5)(2n+4)=0 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 = -6n
2n(-20 + -6n + 2n2) = 0
(-20 * 2n + -6n * 2n + 2n2 * 2n) = 0
(-40n + -12n2 + 4n3) = 0

Solving
-40n + -12n2 + 4n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4n'.
4n(-10 + -3n + n2) = 0

Factor a trinomial.
4n((-2 + -1n)(5 + -1n)) = 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 '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 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 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 3
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

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