(n+2)(n-4)=55

Solution for (n+2)(n-4)=55 equation:

Simplifying
(n + 2)(n + -4) = 55

Reorder the terms:
(2 + n)(n + -4) = 55

Reorder the terms:
(2 + n)(-4 + n) = 55

Multiply (2 + n) * (-4 + n)
(2(-4 + n) + n(-4 + n)) = 55
((-4 * 2 + n * 2) + n(-4 + n)) = 55
((-8 + 2n) + n(-4 + n)) = 55
(-8 + 2n + (-4 * n + n * n)) = 55
(-8 + 2n + (-4n + n2)) = 55

Combine like terms: 2n + -4n = -2n
(-8 + -2n + n2) = 55

Solving
-8 + -2n + n2 = 55

Solving for variable 'n'.

Reorder the terms:
-8 + -55 + -2n + n2 = 55 + -55

Combine like terms: -8 + -55 = -63
-63 + -2n + n2 = 55 + -55

Combine like terms: 55 + -55 = 0
-63 + -2n + n2 = 0

Factor a trinomial.
(-7 + -1n)(9 + -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 '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-7, 9}