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

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

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

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

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

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

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

Remove parenthesis around (-5 + n)
3 + 2n = -5 + n + -1(n + -2)

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

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

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

Combine like terms: n + -1n = 0
3 + 2n = -3 + 0
3 + 2n = -3

Solving
3 + 2n = -3

Solving for variable 'n'.

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

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

Combine like terms: 3 + -3 = 0
0 + 2n = -3 + -3
2n = -3 + -3

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

Divide each side by '2'.
n = -3

Simplifying
n = -3