3n^2=n+2

Solution for 3n^2=n+2 equation:

Simplifying
3n2 = n + 2

Reorder the terms:
3n2 = 2 + n

Solving
3n2 = 2 + n

Solving for variable 'n'.

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

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

Combine like terms: 2 + -2 = 0
-2 + -1n + 3n2 = 0 + n + -1n
-2 + -1n + 3n2 = n + -1n

Combine like terms: n + -1n = 0
-2 + -1n + 3n2 = 0

Factor a trinomial.
(-2 + -3n)(1 + -1n) = 0

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

Simplifying
-2 + -3n = 0

Solving
-2 + -3n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3n = 0 + 2
-3n = 0 + 2

Combine like terms: 0 + 2 = 2
-3n = 2

Divide each side by '-3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Subproblem 2
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
Solution
n = {-0.6666666667, 1}