2n(3n+6)=

Solution for 2n(3n+6)= equation:

Simplifying
2n(3n + 6) = 0

Reorder the terms:
2n(6 + 3n) = 0
(6 * 2n + 3n * 2n) = 0
(12n + 6n2) = 0

Solving
12n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n'.
6n(2 + n) = 0

Ignore the factor 6.
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 + 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, -2}