6(3n+1)=7(9n+3)+6

Solution for 6(3n+1)=7(9n+3)+6 equation:

Simplifying
6(3n + 1) = 7(9n + 3) + 6

Reorder the terms:
6(1 + 3n) = 7(9n + 3) + 6
(1 * 6 + 3n * 6) = 7(9n + 3) + 6
(6 + 18n) = 7(9n + 3) + 6

Reorder the terms:
6 + 18n = 7(3 + 9n) + 6
6 + 18n = (3 * 7 + 9n * 7) + 6
6 + 18n = (21 + 63n) + 6

Reorder the terms:
6 + 18n = 21 + 6 + 63n

Combine like terms: 21 + 6 = 27
6 + 18n = 27 + 63n

Solving
6 + 18n = 27 + 63n

Solving for variable 'n'.

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

Add '-63n' to each side of the equation.
6 + 18n + -63n = 27 + 63n + -63n

Combine like terms: 18n + -63n = -45n
6 + -45n = 27 + 63n + -63n

Combine like terms: 63n + -63n = 0
6 + -45n = 27 + 0
6 + -45n = 27

Add '-6' to each side of the equation.
6 + -6 + -45n = 27 + -6

Combine like terms: 6 + -6 = 0
0 + -45n = 27 + -6
-45n = 27 + -6

Combine like terms: 27 + -6 = 21
-45n = 21

Divide each side by '-45'.
n = -0.4666666667

Simplifying
n = -0.4666666667