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

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

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

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

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

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

Combine like terms: -5n + 3n = -2n
3(-15 + -2n + n2) = 0
(-15 * 3 + -2n * 3 + n2 * 3) = 0
(-45 + -6n + 3n2) = 0

Solving
-45 + -6n + 3n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2n + n2) = 0

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

Ignore the factor 3.
Subproblem 1
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 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 = {-3, 5}