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

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

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

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

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

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

Remove parenthesis around (2 + n)
22 + 3n + n2 = 10 + 2 + n

Combine like terms: 10 + 2 = 12
22 + 3n + n2 = 12 + n

Solving
22 + 3n + n2 = 12 + n

Solving for variable 'n'.

Reorder the terms:
22 + -12 + 3n + -1n + n2 = 12 + n + -12 + -1n

Combine like terms: 22 + -12 = 10
10 + 3n + -1n + n2 = 12 + n + -12 + -1n

Combine like terms: 3n + -1n = 2n
10 + 2n + n2 = 12 + n + -12 + -1n

Reorder the terms:
10 + 2n + n2 = 12 + -12 + n + -1n

Combine like terms: 12 + -12 = 0
10 + 2n + n2 = 0 + n + -1n
10 + 2n + n2 = n + -1n

Combine like terms: n + -1n = 0
10 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 2n + -10 + n2 = 0 + -10

Reorder the terms:
10 + -10 + 2n + n2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 2n + n2 = 0 + -10
2n + n2 = 0 + -10

Combine like terms: 0 + -10 = -10
2n + n2 = -10

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = -10 + 1

Reorder the terms:
1 + 2n + n2 = -10 + 1

Combine like terms: -10 + 1 = -9
1 + 2n + n2 = -9

Factor a perfect square on the left side:
(n + 1)(n + 1) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.