n^2-8n+21=5

Solution for n^2-8n+21=5 equation:

Simplifying
n2 + -8n + 21 = 5

Reorder the terms:
21 + -8n + n2 = 5

Solving
21 + -8n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
21 + -5 + -8n + n2 = 5 + -5

Combine like terms: 21 + -5 = 16
16 + -8n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
16 + -8n + n2 = 0

Factor a trinomial.
(4 + -1n)(4 + -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 '(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
Solution
n = {4, 4}