2n^2+n-820=0

Solution for 2n^2+n-820=0 equation:

Simplifying
2n2 + n + -820 = 0

Reorder the terms:
-820 + n + 2n2 = 0

Solving
-820 + n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-41 + -2n)(20 + -1n) = 0

Subproblem 1
Set the factor '(-41 + -2n)' equal to zero and attempt to solve:

Simplifying
-41 + -2n = 0

Solving
-41 + -2n = 0

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

Add '41' to each side of the equation.
-41 + 41 + -2n = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -2n = 0 + 41
-2n = 0 + 41

Combine like terms: 0 + 41 = 41
-2n = 41

Divide each side by '-2'.
n = -20.5

Simplifying
n = -20.5
Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Solution
n = {-20.5, 20}