3(3n+1)=6(5n+9)+6

Solution for 3(3n+1)=6(5n+9)+6 equation:

Simplifying
3(3n + 1) = 6(5n + 9) + 6

Reorder the terms:
3(1 + 3n) = 6(5n + 9) + 6
(1 * 3 + 3n * 3) = 6(5n + 9) + 6
(3 + 9n) = 6(5n + 9) + 6

Reorder the terms:
3 + 9n = 6(9 + 5n) + 6
3 + 9n = (9 * 6 + 5n * 6) + 6
3 + 9n = (54 + 30n) + 6

Reorder the terms:
3 + 9n = 54 + 6 + 30n

Combine like terms: 54 + 6 = 60
3 + 9n = 60 + 30n

Solving
3 + 9n = 60 + 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.
3 + 9n + -30n = 60 + 30n + -30n

Combine like terms: 9n + -30n = -21n
3 + -21n = 60 + 30n + -30n

Combine like terms: 30n + -30n = 0
3 + -21n = 60 + 0
3 + -21n = 60

Add '-3' to each side of the equation.
3 + -3 + -21n = 60 + -3

Combine like terms: 3 + -3 = 0
0 + -21n = 60 + -3
-21n = 60 + -3

Combine like terms: 60 + -3 = 57
-21n = 57

Divide each side by '-21'.
n = -2.714285714

Simplifying
n = -2.714285714