280=(n+5)(n+5-6)

Solution for 280=(n+5)(n+5-6) equation:

Simplifying
280 = (n + 5)(n + 5 + -6)

Reorder the terms:
280 = (5 + n)(n + 5 + -6)

Reorder the terms:
280 = (5 + n)(5 + -6 + n)

Combine like terms: 5 + -6 = -1
280 = (5 + n)(-1 + n)

Multiply (5 + n) * (-1 + n)
280 = (5(-1 + n) + n(-1 + n))
280 = ((-1 * 5 + n * 5) + n(-1 + n))
280 = ((-5 + 5n) + n(-1 + n))
280 = (-5 + 5n + (-1 * n + n * n))
280 = (-5 + 5n + (-1n + n2))

Combine like terms: 5n + -1n = 4n
280 = (-5 + 4n + n2)

Solving
280 = -5 + 4n + n2

Solving for variable 'n'.

Combine like terms: 280 + 5 = 285
285 + -4n + -1n2 = -5 + 4n + n2 + 5 + -4n + -1n2

Reorder the terms:
285 + -4n + -1n2 = -5 + 5 + 4n + -4n + n2 + -1n2

Combine like terms: -5 + 5 = 0
285 + -4n + -1n2 = 0 + 4n + -4n + n2 + -1n2
285 + -4n + -1n2 = 4n + -4n + n2 + -1n2

Combine like terms: 4n + -4n = 0
285 + -4n + -1n2 = 0 + n2 + -1n2
285 + -4n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
285 + -4n + -1n2 = 0

Factor a trinomial.
(15 + -1n)(19 + n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(19 + n)' equal to zero and attempt to solve:

Simplifying
19 + n = 0

Solving
19 + n = 0

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

Add '-19' to each side of the equation.
19 + -19 + n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + n = 0 + -19
n = 0 + -19

Combine like terms: 0 + -19 = -19
n = -19

Simplifying
n = -19
Solution
n = {15, -19}