n^2-20n+82=7

Solution for n^2-20n+82=7 equation:

Simplifying
n2 + -20n + 82 = 7

Reorder the terms:
82 + -20n + n2 = 7

Solving
82 + -20n + n2 = 7

Solving for variable 'n'.

Reorder the terms:
82 + -7 + -20n + n2 = 7 + -7

Combine like terms: 82 + -7 = 75
75 + -20n + n2 = 7 + -7

Combine like terms: 7 + -7 = 0
75 + -20n + n2 = 0

Factor a trinomial.
(5 + -1n)(15 + -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 '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Solution
n = {5, 15}