(n-12)(n+4)=0

Solution for (n-12)(n+4)=0 equation:

Simplifying
(n + -12)(n + 4) = 0

Reorder the terms:
(-12 + n)(n + 4) = 0

Reorder the terms:
(-12 + n)(4 + n) = 0

Multiply (-12 + n) * (4 + n)
(-12(4 + n) + n(4 + n)) = 0
((4 * -12 + n * -12) + n(4 + n)) = 0
((-48 + -12n) + n(4 + n)) = 0
(-48 + -12n + (4 * n + n * n)) = 0
(-48 + -12n + (4n + n2)) = 0

Combine like terms: -12n + 4n = -8n
(-48 + -8n + n2) = 0

Solving
-48 + -8n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-4 + -1n)(12 + -1n) = 0

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 '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-4, 12}