n^2+18n+53=-3

Solution for n^2+18n+53=-3 equation:

Simplifying
n2 + 18n + 53 = -3

Reorder the terms:
53 + 18n + n2 = -3

Solving
53 + 18n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
53 + 3 + 18n + n2 = -3 + 3

Combine like terms: 53 + 3 = 56
56 + 18n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
56 + 18n + n2 = 0

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

Subproblem 1
Set the factor '(14 + n)' equal to zero and attempt to solve:

Simplifying
14 + n = 0

Solving
14 + n = 0

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

Add '-14' to each side of the equation.
14 + -14 + n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + n = 0 + -14
n = 0 + -14

Combine like terms: 0 + -14 = -14
n = -14

Simplifying
n = -14
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 = {-14, -4}