0=-7n-10-n^2

Solution for 0=-7n-10-n^2 equation:

Simplifying
0 = -7n + -10 + -1n2

Reorder the terms:
0 = -10 + -7n + -1n2

Solving
0 = -10 + -7n + -1n2

Solving for variable 'n'.

Combine like terms: 0 + 10 = 10
10 + 7n + n2 = -10 + -7n + -1n2 + 10 + 7n + n2

Reorder the terms:
10 + 7n + n2 = -10 + 10 + -7n + 7n + -1n2 + n2

Combine like terms: -10 + 10 = 0
10 + 7n + n2 = 0 + -7n + 7n + -1n2 + n2
10 + 7n + n2 = -7n + 7n + -1n2 + n2

Combine like terms: -7n + 7n = 0
10 + 7n + n2 = 0 + -1n2 + n2
10 + 7n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
10 + 7n + n2 = 0

Factor a trinomial.
(5 + n)(2 + n) = 0

Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

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

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {-5, -2}