((n+2)-(n+1))((n+2)+(n+1))=(n-(n+2))(n+(n+2))+25

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Solution for ((n+2)-(n+1))((n+2)+(n+1))=(n-(n+2))(n+(n+2))+25 equation: 


Simplifying
((n + 2) + -1(n + 1))((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Reorder the terms:
((2 + n) + -1(n + 1))((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Remove parenthesis around (2 + n)
(2 + n + -1(n + 1))((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Reorder the terms:
(2 + n + -1(1 + n))((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25
(2 + n + (1 * -1 + n * -1))((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25
(2 + n + (-1 + -1n))((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Reorder the terms:
(2 + -1 + n + -1n)((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Combine like terms: 2 + -1 = 1
(1 + n + -1n)((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Combine like terms: n + -1n = 0
(1 + 0)((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25
(1)((n + 2) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Reorder the terms:
1((2 + n) + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Remove parenthesis around (2 + n)
1(2 + n + (n + 1)) = (n + -1(n + 2))(n + (n + 2)) + 25

Reorder the terms:
1(2 + n + (1 + n)) = (n + -1(n + 2))(n + (n + 2)) + 25

Remove parenthesis around (1 + n)
1(2 + n + 1 + n) = (n + -1(n + 2))(n + (n + 2)) + 25

Reorder the terms:
1(2 + 1 + n + n) = (n + -1(n + 2))(n + (n + 2)) + 25

Combine like terms: 2 + 1 = 3
1(3 + n + n) = (n + -1(n + 2))(n + (n + 2)) + 25

Combine like terms: n + n = 2n
1(3 + 2n) = (n + -1(n + 2))(n + (n + 2)) + 25
(3 * 1 + 2n * 1) = (n + -1(n + 2))(n + (n + 2)) + 25
(3 + 2n) = (n + -1(n + 2))(n + (n + 2)) + 25

Reorder the terms:
3 + 2n = (n + -1(2 + n))(n + (n + 2)) + 25
3 + 2n = (n + (2 * -1 + n * -1))(n + (n + 2)) + 25
3 + 2n = (n + (-2 + -1n))(n + (n + 2)) + 25

Reorder the terms:
3 + 2n = (-2 + n + -1n)(n + (n + 2)) + 25

Combine like terms: n + -1n = 0
3 + 2n = (-2 + 0)(n + (n + 2)) + 25
3 + 2n = (-2)(n + (n + 2)) + 25

Reorder the terms:
3 + 2n = -2(n + (2 + n)) + 25

Remove parenthesis around (2 + n)
3 + 2n = -2(n + 2 + n) + 25

Reorder the terms:
3 + 2n = -2(2 + n + n) + 25

Combine like terms: n + n = 2n
3 + 2n = -2(2 + 2n) + 25
3 + 2n = (2 * -2 + 2n * -2) + 25
3 + 2n = (-4 + -4n) + 25

Reorder the terms:
3 + 2n = -4 + 25 + -4n

Combine like terms: -4 + 25 = 21
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 = 18
6n = 18

Divide each side by '6'.
n = 3

Simplifying
n = 3

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