(n-5)(n+12)=0

Solution for (n-5)(n+12)=0 equation:

Simplifying
(n + -5)(n + 12) = 0

Reorder the terms:
(-5 + n)(n + 12) = 0

Reorder the terms:
(-5 + n)(12 + n) = 0

Multiply (-5 + n) * (12 + n)
(-5(12 + n) + n(12 + n)) = 0
((12 * -5 + n * -5) + n(12 + n)) = 0
((-60 + -5n) + n(12 + n)) = 0
(-60 + -5n + (12 * n + n * n)) = 0
(-60 + -5n + (12n + n2)) = 0

Combine like terms: -5n + 12n = 7n
(-60 + 7n + n2) = 0

Solving
-60 + 7n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-12 + -1n)(5 + -1n) = 0

Subproblem 1
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
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 = {-12, 5}