6n^2=n+2

Solution for 6n^2=n+2 equation:

Simplifying
6n2 = n + 2

Reorder the terms:
6n2 = 2 + n

Solving
6n2 = 2 + n

Solving for variable 'n'.

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

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

Combine like terms: 2 + -2 = 0
-2 + -1n + 6n2 = 0 + n + -1n
-2 + -1n + 6n2 = n + -1n

Combine like terms: n + -1n = 0
-2 + -1n + 6n2 = 0

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

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

Simplifying
-1 + -2n = 0

Solving
-1 + -2n = 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 + -2n = 0 + 1

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

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

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
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
Solution
n = {-0.5, 0.6666666667}