3n^2-2n+1=6

Solution for 3n^2-2n+1=6 equation:

Simplifying
3n2 + -2n + 1 = 6

Reorder the terms:
1 + -2n + 3n2 = 6

Solving
1 + -2n + 3n2 = 6

Solving for variable 'n'.

Reorder the terms:
1 + -6 + -2n + 3n2 = 6 + -6

Combine like terms: 1 + -6 = -5
-5 + -2n + 3n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-5 + -2n + 3n2 = 0

Factor a trinomial.
(-1 + -1n)(5 + -3n) = 0

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 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 + -1n = 0 + 1

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

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 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 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Solution
n = {-1, 1.666666667}