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 = -28
-28 + -3n + n2 = -6 + 6

Combine like terms: -6 + 6 = 0
-28 + -3n + n2 = 0

Factor a trinomial.
(-4 + -1n)(7 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

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

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

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-4, 7}