4(n+6)(n+5)=0

Solution for 4(n+6)(n+5)=0 equation:

Simplifying
4(n + 6)(n + 5) = 0

Reorder the terms:
4(6 + n)(n + 5) = 0

Reorder the terms:
4(6 + n)(5 + n) = 0

Multiply (6 + n) * (5 + n)
4(6(5 + n) + n(5 + n)) = 0
4((5 * 6 + n * 6) + n(5 + n)) = 0
4((30 + 6n) + n(5 + n)) = 0
4(30 + 6n + (5 * n + n * n)) = 0
4(30 + 6n + (5n + n2)) = 0

Combine like terms: 6n + 5n = 11n
4(30 + 11n + n2) = 0
(30 * 4 + 11n * 4 + n2 * 4) = 0
(120 + 44n + 4n2) = 0

Solving
120 + 44n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + 11n + n2) = 0

Factor a trinomial.
4((6 + n)(5 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

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

Simplifying
n = -5
Solution
n = {-6, -5}