2n(3n-3)(n+5)=0

Solution for 2n(3n-3)(n+5)=0 equation:

Simplifying
2n(3n + -3)(n + 5) = 0

Reorder the terms:
2n(-3 + 3n)(n + 5) = 0

Reorder the terms:
2n(-3 + 3n)(5 + n) = 0

Multiply (-3 + 3n) * (5 + n)
2n(-3(5 + n) + 3n * (5 + n)) = 0
2n((5 * -3 + n * -3) + 3n * (5 + n)) = 0
2n((-15 + -3n) + 3n * (5 + n)) = 0
2n(-15 + -3n + (5 * 3n + n * 3n)) = 0
2n(-15 + -3n + (15n + 3n2)) = 0

Combine like terms: -3n + 15n = 12n
2n(-15 + 12n + 3n2) = 0
(-15 * 2n + 12n * 2n + 3n2 * 2n) = 0
(-30n + 24n2 + 6n3) = 0

Solving
-30n + 24n2 + 6n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6n'.
6n(-5 + 4n + n2) = 0

Factor a trinomial.
6n((-5 + -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 '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
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, -5, 1}