4n(2n+6)=0

Solution for 4n(2n+6)=0 equation:

Simplifying
4n(2n + 6) = 0

Reorder the terms:
4n(6 + 2n) = 0
(6 * 4n + 2n * 4n) = 0
(24n + 8n2) = 0

Solving
24n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '8n'.
8n(3 + n) = 0

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

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {0, -3}