3(3n+2)=6(5n+5)+1

Solution for 3(3n+2)=6(5n+5)+1 equation:

Simplifying
3(3n + 2) = 6(5n + 5) + 1

Reorder the terms:
3(2 + 3n) = 6(5n + 5) + 1
(2 * 3 + 3n * 3) = 6(5n + 5) + 1
(6 + 9n) = 6(5n + 5) + 1

Reorder the terms:
6 + 9n = 6(5 + 5n) + 1
6 + 9n = (5 * 6 + 5n * 6) + 1
6 + 9n = (30 + 30n) + 1

Reorder the terms:
6 + 9n = 30 + 1 + 30n

Combine like terms: 30 + 1 = 31
6 + 9n = 31 + 30n

Solving
6 + 9n = 31 + 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 + 9n + -30n = 31 + 30n + -30n

Combine like terms: 9n + -30n = -21n
6 + -21n = 31 + 30n + -30n

Combine like terms: 30n + -30n = 0
6 + -21n = 31 + 0
6 + -21n = 31

Add '-6' to each side of the equation.
6 + -6 + -21n = 31 + -6

Combine like terms: 6 + -6 = 0
0 + -21n = 31 + -6
-21n = 31 + -6

Combine like terms: 31 + -6 = 25
-21n = 25

Divide each side by '-21'.
n = -1.19047619

Simplifying
n = -1.19047619