6(2n+1)=9(3n+1)+2

Solution for 6(2n+1)=9(3n+1)+2 equation:

Simplifying
6(2n + 1) = 9(3n + 1) + 2

Reorder the terms:
6(1 + 2n) = 9(3n + 1) + 2
(1 * 6 + 2n * 6) = 9(3n + 1) + 2
(6 + 12n) = 9(3n + 1) + 2

Reorder the terms:
6 + 12n = 9(1 + 3n) + 2
6 + 12n = (1 * 9 + 3n * 9) + 2
6 + 12n = (9 + 27n) + 2

Reorder the terms:
6 + 12n = 9 + 2 + 27n

Combine like terms: 9 + 2 = 11
6 + 12n = 11 + 27n

Solving
6 + 12n = 11 + 27n

Solving for variable 'n'.

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

Add '-27n' to each side of the equation.
6 + 12n + -27n = 11 + 27n + -27n

Combine like terms: 12n + -27n = -15n
6 + -15n = 11 + 27n + -27n

Combine like terms: 27n + -27n = 0
6 + -15n = 11 + 0
6 + -15n = 11

Add '-6' to each side of the equation.
6 + -6 + -15n = 11 + -6

Combine like terms: 6 + -6 = 0
0 + -15n = 11 + -6
-15n = 11 + -6

Combine like terms: 11 + -6 = 5
-15n = 5

Divide each side by '-15'.
n = -0.3333333333

Simplifying
n = -0.3333333333