n^2+10n+17=-7

Solution for n^2+10n+17=-7 equation:

Simplifying
n2 + 10n + 17 = -7

Reorder the terms:
17 + 10n + n2 = -7

Solving
17 + 10n + n2 = -7

Solving for variable 'n'.

Reorder the terms:
17 + 7 + 10n + n2 = -7 + 7

Combine like terms: 17 + 7 = 24
24 + 10n + n2 = -7 + 7

Combine like terms: -7 + 7 = 0
24 + 10n + n2 = 0

Factor a trinomial.
(6 + n)(4 + n) = 0

Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {-6, -4}