n^2+10n+14=5

Solution for n^2+10n+14=5 equation:

Simplifying
n2 + 10n + 14 = 5

Reorder the terms:
14 + 10n + n2 = 5

Solving
14 + 10n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
14 + -5 + 10n + n2 = 5 + -5

Combine like terms: 14 + -5 = 9
9 + 10n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
9 + 10n + n2 = 0

Factor a trinomial.
(9 + n)(1 + 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 '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-9, -1}