n^2+16n-74=6

Solution for n^2+16n-74=6 equation:

Simplifying
n2 + 16n + -74 = 6

Reorder the terms:
-74 + 16n + n2 = 6

Solving
-74 + 16n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
-74 + -6 + 16n + n2 = 6 + -6

Combine like terms: -74 + -6 = -80
-80 + 16n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-80 + 16n + n2 = 0

Factor a trinomial.
(-20 + -1n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-20 + -1n)' equal to zero and attempt to solve:

Simplifying
-20 + -1n = 0

Solving
-20 + -1n = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1n = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1n = 0 + 20
-1n = 0 + 20

Combine like terms: 0 + 20 = 20
-1n = 20

Divide each side by '-1'.
n = -20

Simplifying
n = -20
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 = {-20, 4}