n^2+16n+52=4

Solution for n^2+16n+52=4 equation:

Simplifying
n2 + 16n + 52 = 4

Reorder the terms:
52 + 16n + n2 = 4

Solving
52 + 16n + n2 = 4

Solving for variable 'n'.

Reorder the terms:
52 + -4 + 16n + n2 = 4 + -4

Combine like terms: 52 + -4 = 48
48 + 16n + n2 = 4 + -4

Combine like terms: 4 + -4 = 0
48 + 16n + n2 = 0

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

Subproblem 1
Set the factor '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 0

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

Add '-12' to each side of the equation.
12 + -12 + n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + n = 0 + -12
n = 0 + -12

Combine like terms: 0 + -12 = -12
n = -12

Simplifying
n = -12
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 = {-12, -4}