n^2-5n+1=7

Solution for n^2-5n+1=7 equation:

Simplifying
n2 + -5n + 1 = 7

Reorder the terms:
1 + -5n + n2 = 7

Solving
1 + -5n + n2 = 7

Solving for variable 'n'.

Reorder the terms:
1 + -7 + -5n + n2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + -5n + n2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + -5n + n2 = 0

Factor a trinomial.
(-1 + -1n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-1, 6}