0=-2n^2+2n+420

Solution for 0=-2n^2+2n+420 equation:

Simplifying
0 = -2n2 + 2n + 420

Reorder the terms:
0 = 420 + 2n + -2n2

Solving
0 = 420 + 2n + -2n2

Solving for variable 'n'.

Combine like terms: 0 + -420 = -420
-420 + -2n + 2n2 = 420 + 2n + -2n2 + -420 + -2n + 2n2

Reorder the terms:
-420 + -2n + 2n2 = 420 + -420 + 2n + -2n + -2n2 + 2n2

Combine like terms: 420 + -420 = 0
-420 + -2n + 2n2 = 0 + 2n + -2n + -2n2 + 2n2
-420 + -2n + 2n2 = 2n + -2n + -2n2 + 2n2

Combine like terms: 2n + -2n = 0
-420 + -2n + 2n2 = 0 + -2n2 + 2n2
-420 + -2n + 2n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
-420 + -2n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-210 + -1n + n2) = 0

Factor a trinomial.
2((-14 + -1n)(15 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Solution
n = {-14, 15}