(n-2)(n+4)=40

Solution for (n-2)(n+4)=40 equation:

Simplifying
(n + -2)(n + 4) = 40

Reorder the terms:
(-2 + n)(n + 4) = 40

Reorder the terms:
(-2 + n)(4 + n) = 40

Multiply (-2 + n) * (4 + n)
(-2(4 + n) + n(4 + n)) = 40
((4 * -2 + n * -2) + n(4 + n)) = 40
((-8 + -2n) + n(4 + n)) = 40
(-8 + -2n + (4 * n + n * n)) = 40
(-8 + -2n + (4n + n2)) = 40

Combine like terms: -2n + 4n = 2n
(-8 + 2n + n2) = 40

Solving
-8 + 2n + n2 = 40

Solving for variable 'n'.

Reorder the terms:
-8 + -40 + 2n + n2 = 40 + -40

Combine like terms: -8 + -40 = -48
-48 + 2n + n2 = 40 + -40

Combine like terms: 40 + -40 = 0
-48 + 2n + n2 = 0

Factor a trinomial.
(-8 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-8, 6}