3(n-3)(n+3n)=0

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

Simplifying
3(n + -3)(n + 3n) = 0

Reorder the terms:
3(-3 + n)(n + 3n) = 0

Combine like terms: n + 3n = 4n
3(-3 + n)(4n) = 0

Remove parenthesis around (4n)
3(-3 + n) * 4n = 0

Reorder the terms for easier multiplication:
3 * 4n(-3 + n) = 0

Multiply 3 * 4
12n(-3 + n) = 0
(-3 * 12n + n * 12n) = 0
(-36n + 12n2) = 0

Solving
-36n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '12n'.
12n(-3 + n) = 0

Ignore the factor 12.
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}