63=2n+1(n+1)+1+2(n+2)+1

Solution for 63=2n+1(n+1)+1+2(n+2)+1 equation:

Simplifying
63 = 2n + 1(n + 1) + 1 + 2(n + 2) + 1

Reorder the terms:
63 = 2n + 1(1 + n) + 1 + 2(n + 2) + 1
63 = 2n + (1 * 1 + n * 1) + 1 + 2(n + 2) + 1
63 = 2n + (1 + 1n) + 1 + 2(n + 2) + 1

Reorder the terms:
63 = 2n + 1 + 1n + 1 + 2(2 + n) + 1
63 = 2n + 1 + 1n + 1 + (2 * 2 + n * 2) + 1
63 = 2n + 1 + 1n + 1 + (4 + 2n) + 1

Reorder the terms:
63 = 1 + 1 + 4 + 1 + 2n + 1n + 2n

Combine like terms: 1 + 1 = 2
63 = 2 + 4 + 1 + 2n + 1n + 2n

Combine like terms: 2 + 4 = 6
63 = 6 + 1 + 2n + 1n + 2n

Combine like terms: 6 + 1 = 7
63 = 7 + 2n + 1n + 2n

Combine like terms: 2n + 1n = 3n
63 = 7 + 3n + 2n

Combine like terms: 3n + 2n = 5n
63 = 7 + 5n

Solving
63 = 7 + 5n

Solving for variable 'n'.

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

Add '-5n' to each side of the equation.
63 + -5n = 7 + 5n + -5n

Combine like terms: 5n + -5n = 0
63 + -5n = 7 + 0
63 + -5n = 7

Add '-63' to each side of the equation.
63 + -63 + -5n = 7 + -63

Combine like terms: 63 + -63 = 0
0 + -5n = 7 + -63
-5n = 7 + -63

Combine like terms: 7 + -63 = -56
-5n = -56

Divide each side by '-5'.
n = 11.2

Simplifying
n = 11.2