3(n+1)=2(n+3)-6

Solution for 3(n+1)=2(n+3)-6 equation:

Simplifying
3(n + 1) = 2(n + 3) + -6

Reorder the terms:
3(1 + n) = 2(n + 3) + -6
(1 * 3 + n * 3) = 2(n + 3) + -6
(3 + 3n) = 2(n + 3) + -6

Reorder the terms:
3 + 3n = 2(3 + n) + -6
3 + 3n = (3 * 2 + n * 2) + -6
3 + 3n = (6 + 2n) + -6

Reorder the terms:
3 + 3n = 6 + -6 + 2n

Combine like terms: 6 + -6 = 0
3 + 3n = 0 + 2n
3 + 3n = 2n

Solving
3 + 3n = 2n

Solving for variable 'n'.

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

Add '-2n' to each side of the equation.
3 + 3n + -2n = 2n + -2n

Combine like terms: 3n + -2n = 1n
3 + 1n = 2n + -2n

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

Add '-3' to each side of the equation.
3 + -3 + 1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 1n = 0 + -3
1n = 0 + -3

Combine like terms: 0 + -3 = -3
1n = -3

Divide each side by '1'.
n = -3

Simplifying
n = -3