-504=n(-2n-18)

Solution for -504=n(-2n-18) equation:

Simplifying
-504 = n(-2n + -18)

Reorder the terms:
-504 = n(-18 + -2n)
-504 = (-18 * n + -2n * n)
-504 = (-18n + -2n2)

Solving
-504 = -18n + -2n2

Solving for variable 'n'.

Reorder the terms:
-504 + 18n + 2n2 = -18n + 18n + -2n2 + 2n2

Combine like terms: -18n + 18n = 0
-504 + 18n + 2n2 = 0 + -2n2 + 2n2
-504 + 18n + 2n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
-504 + 18n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-252 + 9n + n2) = 0

Factor a trinomial.
2((-21 + -1n)(12 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -1n)' equal to zero and attempt to solve:

Simplifying
-21 + -1n = 0

Solving
-21 + -1n = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1n = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1n = 0 + 21
-1n = 0 + 21

Combine like terms: 0 + 21 = 21
-1n = 21

Divide each side by '-1'.
n = -21

Simplifying
n = -21
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-21, 12}