3n(6n+3)=0

Solution for 3n(6n+3)=0 equation:

Simplifying
3n(6n + 3) = 0

Reorder the terms:
3n(3 + 6n) = 0
(3 * 3n + 6n * 3n) = 0
(9n + 18n2) = 0

Solving
9n + 18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '9n'.
9n(1 + 2n) = 0

Ignore the factor 9.
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 '(1 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2n = 0 + -1

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

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

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {0, -0.5}