6n(3n+2)=

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

Simplifying
6n(3n + 2) = 0

Reorder the terms:
6n(2 + 3n) = 0
(2 * 6n + 3n * 6n) = 0
(12n + 18n2) = 0

Solving
12n + 18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n'.
6n(2 + 3n) = 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 + 3n)' equal to zero and attempt to solve:

Simplifying
2 + 3n = 0

Solving
2 + 3n = 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 + 3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3n = 0 + -2
3n = 0 + -2

Combine like terms: 0 + -2 = -2
3n = -2

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Solution
n = {0, -0.6666666667}