2n^2+n-406=0

Solution for 2n^2+n-406=0 equation:

Simplifying
2n2 + n + -406 = 0

Reorder the terms:
-406 + n + 2n2 = 0

Solving
-406 + n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-29 + -2n)(14 + -1n) = 0

Subproblem 1
Set the factor '(-29 + -2n)' equal to zero and attempt to solve:

Simplifying
-29 + -2n = 0

Solving
-29 + -2n = 0

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

Add '29' to each side of the equation.
-29 + 29 + -2n = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -2n = 0 + 29
-2n = 0 + 29

Combine like terms: 0 + 29 = 29
-2n = 29

Divide each side by '-2'.
n = -14.5

Simplifying
n = -14.5
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {-14.5, 14}