(n-12)(n+5)=

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

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

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

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

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

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

Solving
-60 + -7n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
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 = {-5, 12}