=3n^2-17n-6

Solution for =3n^2-17n-6 equation:

Simplifying
0 = 3n2 + -17n + -6

Reorder the terms:
0 = -6 + -17n + 3n2

Solving
0 = -6 + -17n + 3n2

Solving for variable 'n'.

Combine like terms: 0 + 6 = 6
6 + 17n + -3n2 = -6 + -17n + 3n2 + 6 + 17n + -3n2

Reorder the terms:
6 + 17n + -3n2 = -6 + 6 + -17n + 17n + 3n2 + -3n2

Combine like terms: -6 + 6 = 0
6 + 17n + -3n2 = 0 + -17n + 17n + 3n2 + -3n2
6 + 17n + -3n2 = -17n + 17n + 3n2 + -3n2

Combine like terms: -17n + 17n = 0
6 + 17n + -3n2 = 0 + 3n2 + -3n2
6 + 17n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
6 + 17n + -3n2 = 0

Factor a trinomial.
(6 + -1n)(1 + 3n) = 0

Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(1 + 3n)' equal to zero and attempt to solve:

Simplifying
1 + 3n = 0

Solving
1 + 3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3n = 0 + -1
3n = 0 + -1

Combine like terms: 0 + -1 = -1
3n = -1

Divide each side by '3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Solution
n = {6, -0.3333333333}