(2n-4)(n+6)=936

Solution for (2n-4)(n+6)=936 equation:

Simplifying
(2n + -4)(n + 6) = 936

Reorder the terms:
(-4 + 2n)(n + 6) = 936

Reorder the terms:
(-4 + 2n)(6 + n) = 936

Multiply (-4 + 2n) * (6 + n)
(-4(6 + n) + 2n * (6 + n)) = 936
((6 * -4 + n * -4) + 2n * (6 + n)) = 936
((-24 + -4n) + 2n * (6 + n)) = 936
(-24 + -4n + (6 * 2n + n * 2n)) = 936
(-24 + -4n + (12n + 2n2)) = 936

Combine like terms: -4n + 12n = 8n
(-24 + 8n + 2n2) = 936

Solving
-24 + 8n + 2n2 = 936

Solving for variable 'n'.

Reorder the terms:
-24 + -936 + 8n + 2n2 = 936 + -936

Combine like terms: -24 + -936 = -960
-960 + 8n + 2n2 = 936 + -936

Combine like terms: 936 + -936 = 0
-960 + 8n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-480 + 4n + n2) = 0

Factor a trinomial.
2((-24 + -1n)(20 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + -1n)' equal to zero and attempt to solve:

Simplifying
-24 + -1n = 0

Solving
-24 + -1n = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1n = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1n = 0 + 24
-1n = 0 + 24

Combine like terms: 0 + 24 = 24
-1n = 24

Divide each side by '-1'.
n = -24

Simplifying
n = -24
Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Solution
n = {-24, 20}