n^2-61n+280=0

Solution for n^2-61n+280=0 equation:

Simplifying
n2 + -61n + 280 = 0

Reorder the terms:
280 + -61n + n2 = 0

Solving
280 + -61n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + -1n)(56 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(56 + -1n)' equal to zero and attempt to solve:

Simplifying
56 + -1n = 0

Solving
56 + -1n = 0

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

Add '-56' to each side of the equation.
56 + -56 + -1n = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -1n = 0 + -56
-1n = 0 + -56

Combine like terms: 0 + -56 = -56
-1n = -56

Divide each side by '-1'.
n = 56

Simplifying
n = 56
Solution
n = {5, 56}