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

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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.
(-5 + -1n)(7 + -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 '(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
Solution
n = {-5, 7}

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