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

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

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

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

Reorder the terms:
6 + 18n = 6(6 + 5n) + 3
6 + 18n = (6 * 6 + 5n * 6) + 3
6 + 18n = (36 + 30n) + 3

Reorder the terms:
6 + 18n = 36 + 3 + 30n

Combine like terms: 36 + 3 = 39
6 + 18n = 39 + 30n

Solving
6 + 18n = 39 + 30n

Solving for variable 'n'.

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

Add '-30n' to each side of the equation.
6 + 18n + -30n = 39 + 30n + -30n

Combine like terms: 18n + -30n = -12n
6 + -12n = 39 + 30n + -30n

Combine like terms: 30n + -30n = 0
6 + -12n = 39 + 0
6 + -12n = 39

Add '-6' to each side of the equation.
6 + -6 + -12n = 39 + -6

Combine like terms: 6 + -6 = 0
0 + -12n = 39 + -6
-12n = 39 + -6

Combine like terms: 39 + -6 = 33
-12n = 33

Divide each side by '-12'.
n = -2.75

Simplifying
n = -2.75