n^2+13n+21=5+5n

Solution for n^2+13n+21=5+5n equation:

Simplifying
n2 + 13n + 21 = 5 + 5n

Reorder the terms:
21 + 13n + n2 = 5 + 5n

Solving
21 + 13n + n2 = 5 + 5n

Solving for variable 'n'.

Reorder the terms:
21 + -5 + 13n + -5n + n2 = 5 + 5n + -5 + -5n

Combine like terms: 21 + -5 = 16
16 + 13n + -5n + n2 = 5 + 5n + -5 + -5n

Combine like terms: 13n + -5n = 8n
16 + 8n + n2 = 5 + 5n + -5 + -5n

Reorder the terms:
16 + 8n + n2 = 5 + -5 + 5n + -5n

Combine like terms: 5 + -5 = 0
16 + 8n + n2 = 0 + 5n + -5n
16 + 8n + n2 = 5n + -5n

Combine like terms: 5n + -5n = 0
16 + 8n + n2 = 0

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

Subproblem 1
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
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 = {-4, -4}