n^2-18n-83=5

Solution for n^2-18n-83=5 equation:

Simplifying
n2 + -18n + -83 = 5

Reorder the terms:
-83 + -18n + n2 = 5

Solving
-83 + -18n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
-83 + -5 + -18n + n2 = 5 + -5

Combine like terms: -83 + -5 = -88
-88 + -18n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-88 + -18n + n2 = 0

Factor a trinomial.
(-4 + -1n)(22 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(22 + -1n)' equal to zero and attempt to solve:

Simplifying
22 + -1n = 0

Solving
22 + -1n = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1n = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1n = 0 + -22
-1n = 0 + -22

Combine like terms: 0 + -22 = -22
-1n = -22

Divide each side by '-1'.
n = 22

Simplifying
n = 22
Solution
n = {-4, 22}