3(n+4)(n-5)=0

Solution for 3(n+4)(n-5)=0 equation:

Simplifying
3(n + 4)(n + -5) = 0

Reorder the terms:
3(4 + n)(n + -5) = 0

Reorder the terms:
3(4 + n)(-5 + n) = 0

Multiply (4 + n) * (-5 + n)
3(4(-5 + n) + n(-5 + n)) = 0
3((-5 * 4 + n * 4) + n(-5 + n)) = 0
3((-20 + 4n) + n(-5 + n)) = 0
3(-20 + 4n + (-5 * n + n * n)) = 0
3(-20 + 4n + (-5n + n2)) = 0

Combine like terms: 4n + -5n = -1n
3(-20 + -1n + n2) = 0
(-20 * 3 + -1n * 3 + n2 * 3) = 0
(-60 + -3n + 3n2) = 0

Solving
-60 + -3n + 3n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -1n + n2) = 0

Factor a trinomial.
3((-4 + -1n)(5 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
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
Solution
n = {-4, 5}