6((-1+-1n)(4+-1n))=0

Solution for 6((-1+-1n)(4+-1n))=0 equation:

Simplifying
6((-1 + -1n)(4 + -1n)) = 0

Multiply (-1 + -1n) * (4 + -1n)
6((-1(4 + -1n) + -1n * (4 + -1n))) = 0
6(((4 * -1 + -1n * -1) + -1n * (4 + -1n))) = 0
6(((-4 + 1n) + -1n * (4 + -1n))) = 0
6((-4 + 1n + (4 * -1n + -1n * -1n))) = 0
6((-4 + 1n + (-4n + 1n2))) = 0

Combine like terms: 1n + -4n = -3n
6((-4 + -3n + 1n2)) = 0
(-4 * 6 + -3n * 6 + 1n2 * 6) = 0
(-24 + -18n + 6n2) = 0

Solving
-24 + -18n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -3n + n2) = 0

Factor a trinomial.
6((-1 + -1n)(4 + -1n)) = 0

Ignore the factor 6.
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 '(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
Solution
n = {-1, 4}