2n+2+1=2(n-3)-3(5+2n)

Solution for 2n+2+1=2(n-3)-3(5+2n) equation:

Simplifying
2n + 2 + 1 = 2(n + -3) + -3(5 + 2n)

Reorder the terms:
2 + 1 + 2n = 2(n + -3) + -3(5 + 2n)

Combine like terms: 2 + 1 = 3
3 + 2n = 2(n + -3) + -3(5 + 2n)

Reorder the terms:
3 + 2n = 2(-3 + n) + -3(5 + 2n)
3 + 2n = (-3 * 2 + n * 2) + -3(5 + 2n)
3 + 2n = (-6 + 2n) + -3(5 + 2n)
3 + 2n = -6 + 2n + (5 * -3 + 2n * -3)
3 + 2n = -6 + 2n + (-15 + -6n)

Reorder the terms:
3 + 2n = -6 + -15 + 2n + -6n

Combine like terms: -6 + -15 = -21
3 + 2n = -21 + 2n + -6n

Combine like terms: 2n + -6n = -4n
3 + 2n = -21 + -4n

Solving
3 + 2n = -21 + -4n

Solving for variable 'n'.

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

Add '4n' to each side of the equation.
3 + 2n + 4n = -21 + -4n + 4n

Combine like terms: 2n + 4n = 6n
3 + 6n = -21 + -4n + 4n

Combine like terms: -4n + 4n = 0
3 + 6n = -21 + 0
3 + 6n = -21

Add '-3' to each side of the equation.
3 + -3 + 6n = -21 + -3

Combine like terms: 3 + -3 = 0
0 + 6n = -21 + -3
6n = -21 + -3

Combine like terms: -21 + -3 = -24
6n = -24

Divide each side by '6'.
n = -4

Simplifying
n = -4