(n)(n)+72=-17n

Solution for (n)(n)+72=-17n equation:

Simplifying
(n)(n) + 72 = -17n

Multiply n * n
n2 + 72 = -17n

Reorder the terms:
72 + n2 = -17n

Solving
72 + n2 = -17n

Solving for variable 'n'.

Reorder the terms:
72 + 17n + n2 = -17n + 17n

Combine like terms: -17n + 17n = 0
72 + 17n + n2 = 0

Factor a trinomial.
(9 + n)(8 + n) = 0

Subproblem 1
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Subproblem 2
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Solution
n = {-9, -8}