4(n+1)(n-5)=0

Solution for 4(n+1)(n-5)=0 equation:

Simplifying
4(n + 1)(n + -5) = 0

Reorder the terms:
4(1 + n)(n + -5) = 0

Reorder the terms:
4(1 + n)(-5 + n) = 0

Multiply (1 + n) * (-5 + n)
4(1(-5 + n) + n(-5 + n)) = 0
4((-5 * 1 + n * 1) + n(-5 + n)) = 0
4((-5 + 1n) + n(-5 + n)) = 0
4(-5 + 1n + (-5 * n + n * n)) = 0
4(-5 + 1n + (-5n + n2)) = 0

Combine like terms: 1n + -5n = -4n
4(-5 + -4n + n2) = 0
(-5 * 4 + -4n * 4 + n2 * 4) = 0
(-20 + -16n + 4n2) = 0

Solving
-20 + -16n + 4n2 = 0

Solving for variable 'n'.

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

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

Ignore the factor 4.
Subproblem 1
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
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 = {-1, 5}