6(n+1)=3(6+n)+5n

Solution for 6(n+1)=3(6+n)+5n equation:

Simplifying
6(n + 1) = 3(6 + n) + 5n

Reorder the terms:
6(1 + n) = 3(6 + n) + 5n
(1 * 6 + n * 6) = 3(6 + n) + 5n
(6 + 6n) = 3(6 + n) + 5n
6 + 6n = (6 * 3 + n * 3) + 5n
6 + 6n = (18 + 3n) + 5n

Combine like terms: 3n + 5n = 8n
6 + 6n = 18 + 8n

Solving
6 + 6n = 18 + 8n

Solving for variable 'n'.

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

Add '-8n' to each side of the equation.
6 + 6n + -8n = 18 + 8n + -8n

Combine like terms: 6n + -8n = -2n
6 + -2n = 18 + 8n + -8n

Combine like terms: 8n + -8n = 0
6 + -2n = 18 + 0
6 + -2n = 18

Add '-6' to each side of the equation.
6 + -6 + -2n = 18 + -6

Combine like terms: 6 + -6 = 0
0 + -2n = 18 + -6
-2n = 18 + -6

Combine like terms: 18 + -6 = 12
-2n = 12

Divide each side by '-2'.
n = -6

Simplifying
n = -6