6n(n-1)(n+3)=

Solution for 6n(n-1)(n+3)= equation:

Simplifying
6n(n + -1)(n + 3) = 0

Reorder the terms:
6n(-1 + n)(n + 3) = 0

Reorder the terms:
6n(-1 + n)(3 + n) = 0

Multiply (-1 + n) * (3 + n)
6n(-1(3 + n) + n(3 + n)) = 0
6n((3 * -1 + n * -1) + n(3 + n)) = 0
6n((-3 + -1n) + n(3 + n)) = 0
6n(-3 + -1n + (3 * n + n * n)) = 0
6n(-3 + -1n + (3n + n2)) = 0

Combine like terms: -1n + 3n = 2n
6n(-3 + 2n + n2) = 0
(-3 * 6n + 2n * 6n + n2 * 6n) = 0
(-18n + 12n2 + 6n3) = 0

Solving
-18n + 12n2 + 6n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n'.
6n(-3 + 2n + n2) = 0

Factor a trinomial.
6n((-3 + -1n)(1 + -1n)) = 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 '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 3
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {0, -3, 1}