n^2-3n-34=6

Solution for n^2-3n-34=6 equation:

Simplifying
n2 + -3n + -34 = 6

Reorder the terms:
-34 + -3n + n2 = 6

Solving
-34 + -3n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
-34 + -6 + -3n + n2 = 6 + -6

Combine like terms: -34 + -6 = -40
-40 + -3n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-40 + -3n + n2 = 0

Factor a trinomial.
(-5 + -1n)(8 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
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
Solution
n = {-5, 8}