3n^2-4n-34=-2

Solution for 3n^2-4n-34=-2 equation:

Simplifying
3n2 + -4n + -34 = -2

Reorder the terms:
-34 + -4n + 3n2 = -2

Solving
-34 + -4n + 3n2 = -2

Solving for variable 'n'.

Reorder the terms:
-34 + 2 + -4n + 3n2 = -2 + 2

Combine like terms: -34 + 2 = -32
-32 + -4n + 3n2 = -2 + 2

Combine like terms: -2 + 2 = 0
-32 + -4n + 3n2 = 0

Factor a trinomial.
(-8 + -3n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve:

Simplifying
-8 + -3n = 0

Solving
-8 + -3n = 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 + -3n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3n = 0 + 8
-3n = 0 + 8

Combine like terms: 0 + 8 = 8
-3n = 8

Divide each side by '-3'.
n = -2.666666667

Simplifying
n = -2.666666667
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 = {-2.666666667, 4}