n^2-2n-74=6

Solution for n^2-2n-74=6 equation:

Simplifying
n2 + -2n + -74 = 6

Reorder the terms:
-74 + -2n + n2 = 6

Solving
-74 + -2n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
-74 + -6 + -2n + n2 = 6 + -6

Combine like terms: -74 + -6 = -80
-80 + -2n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-80 + -2n + n2 = 0

Factor a trinomial.
(-8 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-8, 10}