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

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

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

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

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

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

Combine like terms: 10 + -2 = 8
22 + 3n + n2 = 8 + -1n

Solving
22 + 3n + n2 = 8 + -1n

Solving for variable 'n'.

Reorder the terms:
22 + -8 + 3n + n + n2 = 8 + -1n + -8 + n

Combine like terms: 22 + -8 = 14
14 + 3n + n + n2 = 8 + -1n + -8 + n

Combine like terms: 3n + n = 4n
14 + 4n + n2 = 8 + -1n + -8 + n

Reorder the terms:
14 + 4n + n2 = 8 + -8 + -1n + n

Combine like terms: 8 + -8 = 0
14 + 4n + n2 = 0 + -1n + n
14 + 4n + n2 = -1n + n

Combine like terms: -1n + n = 0
14 + 4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 4n + -14 + n2 = 0 + -14

Reorder the terms:
14 + -14 + 4n + n2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 4n + n2 = 0 + -14
4n + n2 = 0 + -14

Combine like terms: 0 + -14 = -14
4n + n2 = -14

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = -14 + 4

Reorder the terms:
4 + 4n + n2 = -14 + 4

Combine like terms: -14 + 4 = -10
4 + 4n + n2 = -10

Factor a perfect square on the left side:
(n + 2)(n + 2) = -10

Can't calculate square root of the right side.

The solution to this equation could not be determined.