(n-2)(n+4)=27

Solution for (n-2)(n+4)=27 equation:

Simplifying
(n + -2)(n + 4) = 27

Reorder the terms:
(-2 + n)(n + 4) = 27

Reorder the terms:
(-2 + n)(4 + n) = 27

Multiply (-2 + n) * (4 + n)
(-2(4 + n) + n(4 + n)) = 27
((4 * -2 + n * -2) + n(4 + n)) = 27
((-8 + -2n) + n(4 + n)) = 27
(-8 + -2n + (4 * n + n * n)) = 27
(-8 + -2n + (4n + n2)) = 27

Combine like terms: -2n + 4n = 2n
(-8 + 2n + n2) = 27

Solving
-8 + 2n + n2 = 27

Solving for variable 'n'.

Reorder the terms:
-8 + -27 + 2n + n2 = 27 + -27

Combine like terms: -8 + -27 = -35
-35 + 2n + n2 = 27 + -27

Combine like terms: 27 + -27 = 0
-35 + 2n + n2 = 0

Factor a trinomial.
(-7 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
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 = {-7, 5}