10n^2+n=255

Solution for 10n^2+n=255 equation:

Simplifying
10n2 + n = 255

Reorder the terms:
n + 10n2 = 255

Solving
n + 10n2 = 255

Solving for variable 'n'.

Reorder the terms:
-255 + n + 10n2 = 255 + -255

Combine like terms: 255 + -255 = 0
-255 + n + 10n2 = 0

Factor a trinomial.
(-51 + -10n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-51 + -10n)' equal to zero and attempt to solve:

Simplifying
-51 + -10n = 0

Solving
-51 + -10n = 0

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

Add '51' to each side of the equation.
-51 + 51 + -10n = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -10n = 0 + 51
-10n = 0 + 51

Combine like terms: 0 + 51 = 51
-10n = 51

Divide each side by '-10'.
n = -5.1

Simplifying
n = -5.1
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-5.1, 5}