n^2-8n+1=-6

Solution for n^2-8n+1=-6 equation:

Simplifying
n2 + -8n + 1 = -6

Reorder the terms:
1 + -8n + n2 = -6

Solving
1 + -8n + n2 = -6

Solving for variable 'n'.

Reorder the terms:
1 + 6 + -8n + n2 = -6 + 6

Combine like terms: 1 + 6 = 7
7 + -8n + n2 = -6 + 6

Combine like terms: -6 + 6 = 0
7 + -8n + n2 = 0

Factor a trinomial.
(1 + -1n)(7 + -1n) = 0

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {1, 7}