0=7n-6-n^2

Solution for 0=7n-6-n^2 equation:

Simplifying
0 = 7n + -6 + -1n2

Reorder the terms:
0 = -6 + 7n + -1n2

Solving
0 = -6 + 7n + -1n2

Solving for variable 'n'.

Combine like terms: 0 + 6 = 6
6 + -7n + n2 = -6 + 7n + -1n2 + 6 + -7n + n2

Reorder the terms:
6 + -7n + n2 = -6 + 6 + 7n + -7n + -1n2 + n2

Combine like terms: -6 + 6 = 0
6 + -7n + n2 = 0 + 7n + -7n + -1n2 + n2
6 + -7n + n2 = 7n + -7n + -1n2 + n2

Combine like terms: 7n + -7n = 0
6 + -7n + n2 = 0 + -1n2 + n2
6 + -7n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
6 + -7n + 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}