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

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

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

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

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

Multiply (3 + n) * (3 + 2n)
(3(3 + 2n) + n(3 + 2n)) = (n + 2) + (n + -2)
((3 * 3 + 2n * 3) + n(3 + 2n)) = (n + 2) + (n + -2)
((9 + 6n) + n(3 + 2n)) = (n + 2) + (n + -2)
(9 + 6n + (3 * n + 2n * n)) = (n + 2) + (n + -2)
(9 + 6n + (3n + 2n2)) = (n + 2) + (n + -2)

Combine like terms: 6n + 3n = 9n
(9 + 9n + 2n2) = (n + 2) + (n + -2)

Reorder the terms:
9 + 9n + 2n2 = (2 + n) + (n + -2)

Remove parenthesis around (2 + n)
9 + 9n + 2n2 = 2 + n + (n + -2)

Reorder the terms:
9 + 9n + 2n2 = 2 + n + (-2 + n)

Remove parenthesis around (-2 + n)
9 + 9n + 2n2 = 2 + n + -2 + n

Reorder the terms:
9 + 9n + 2n2 = 2 + -2 + n + n

Combine like terms: 2 + -2 = 0
9 + 9n + 2n2 = 0 + n + n
9 + 9n + 2n2 = n + n

Combine like terms: n + n = 2n
9 + 9n + 2n2 = 2n

Solving
9 + 9n + 2n2 = 2n

Solving for variable 'n'.

Reorder the terms:
9 + 9n + -2n + 2n2 = 2n + -2n

Combine like terms: 9n + -2n = 7n
9 + 7n + 2n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
9 + 7n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
4.5 + 3.5n + n2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 3.5n + -4.5 + n2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 3.5n + n2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 3.5n + n2 = 0 + -4.5
3.5n + n2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
3.5n + n2 = -4.5

The n term is 3.5n.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5n + 3.0625 + n2 = -4.5 + 3.0625

Reorder the terms:
3.0625 + 3.5n + n2 = -4.5 + 3.0625

Combine like terms: -4.5 + 3.0625 = -1.4375
3.0625 + 3.5n + n2 = -1.4375

Factor a perfect square on the left side:
(n + 1.75)(n + 1.75) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.