n^2+14n+37=-3

Solution for n^2+14n+37=-3 equation:

Simplifying
n2 + 14n + 37 = -3

Reorder the terms:
37 + 14n + n2 = -3

Solving
37 + 14n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
37 + 3 + 14n + n2 = -3 + 3

Combine like terms: 37 + 3 = 40
40 + 14n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
40 + 14n + n2 = 0

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

Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

Add '-10' to each side of the equation.
10 + -10 + n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n = 0 + -10
n = 0 + -10

Combine like terms: 0 + -10 = -10
n = -10

Simplifying
n = -10
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 = {-10, -4}