((n+1)-n)((n+1)+(n+2))=-7

Solution for ((n+1)-n)((n+1)+(n+2))=-7 equation:

Simplifying
((n + 1) + -1n)((n + 1) + (n + 2)) = -7

Reorder the terms:
((1 + n) + -1n)((n + 1) + (n + 2)) = -7

Remove parenthesis around (1 + n)
(1 + n + -1n)((n + 1) + (n + 2)) = -7

Combine like terms: n + -1n = 0
(1 + 0)((n + 1) + (n + 2)) = -7
(1)((n + 1) + (n + 2)) = -7

Reorder the terms:
1((1 + n) + (n + 2)) = -7

Remove parenthesis around (1 + n)
1(1 + n + (n + 2)) = -7

Reorder the terms:
1(1 + n + (2 + n)) = -7

Remove parenthesis around (2 + n)
1(1 + n + 2 + n) = -7

Reorder the terms:
1(1 + 2 + n + n) = -7

Combine like terms: 1 + 2 = 3
1(3 + n + n) = -7

Combine like terms: n + n = 2n
1(3 + 2n) = -7
(3 * 1 + 2n * 1) = -7
(3 + 2n) = -7

Solving
3 + 2n = -7

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 = -7 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = -7 + -3
2n = -7 + -3

Combine like terms: -7 + -3 = -10
2n = -10

Divide each side by '2'.
n = -5

Simplifying
n = -5