n^2+6n+8=10n+20

Solution for n^2+6n+8=10n+20 equation:

Simplifying
n2 + 6n + 8 = 10n + 20

Reorder the terms:
8 + 6n + n2 = 10n + 20

Reorder the terms:
8 + 6n + n2 = 20 + 10n

Solving
8 + 6n + n2 = 20 + 10n

Solving for variable 'n'.

Reorder the terms:
8 + -20 + 6n + -10n + n2 = 20 + 10n + -20 + -10n

Combine like terms: 8 + -20 = -12
-12 + 6n + -10n + n2 = 20 + 10n + -20 + -10n

Combine like terms: 6n + -10n = -4n
-12 + -4n + n2 = 20 + 10n + -20 + -10n

Reorder the terms:
-12 + -4n + n2 = 20 + -20 + 10n + -10n

Combine like terms: 20 + -20 = 0
-12 + -4n + n2 = 0 + 10n + -10n
-12 + -4n + n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-12 + -4n + n2 = 0

Factor a trinomial.
(-2 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-2, 6}