n*(n+3)+22=10*(-n-2)

Solution for n*(n+3)+22=10*(-n-2) equation:

Simplifying
n(n + 3) + 22 = 10(-1n + -2)

Reorder the terms:
n(3 + n) + 22 = 10(-1n + -2)
(3 * n + n * n) + 22 = 10(-1n + -2)
(3n + n2) + 22 = 10(-1n + -2)

Reorder the terms:
22 + 3n + n2 = 10(-1n + -2)

Reorder the terms:
22 + 3n + n2 = 10(-2 + -1n)
22 + 3n + n2 = (-2 * 10 + -1n * 10)
22 + 3n + n2 = (-20 + -10n)

Solving
22 + 3n + n2 = -20 + -10n

Solving for variable 'n'.

Reorder the terms:
22 + 20 + 3n + 10n + n2 = -20 + -10n + 20 + 10n

Combine like terms: 22 + 20 = 42
42 + 3n + 10n + n2 = -20 + -10n + 20 + 10n

Combine like terms: 3n + 10n = 13n
42 + 13n + n2 = -20 + -10n + 20 + 10n

Reorder the terms:
42 + 13n + n2 = -20 + 20 + -10n + 10n

Combine like terms: -20 + 20 = 0
42 + 13n + n2 = 0 + -10n + 10n
42 + 13n + n2 = -10n + 10n

Combine like terms: -10n + 10n = 0
42 + 13n + n2 = 0

Factor a trinomial.
(7 + n)(6 + n) = 0

Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

Simplifying
n = -6
Solution
n = {-7, -6}