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

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

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

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

Reorder the terms:
3 + 9n = 9(1 + 5n) + 1
3 + 9n = (1 * 9 + 5n * 9) + 1
3 + 9n = (9 + 45n) + 1

Reorder the terms:
3 + 9n = 9 + 1 + 45n

Combine like terms: 9 + 1 = 10
3 + 9n = 10 + 45n

Solving
3 + 9n = 10 + 45n

Solving for variable 'n'.

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

Add '-45n' to each side of the equation.
3 + 9n + -45n = 10 + 45n + -45n

Combine like terms: 9n + -45n = -36n
3 + -36n = 10 + 45n + -45n

Combine like terms: 45n + -45n = 0
3 + -36n = 10 + 0
3 + -36n = 10

Add '-3' to each side of the equation.
3 + -3 + -36n = 10 + -3

Combine like terms: 3 + -3 = 0
0 + -36n = 10 + -3
-36n = 10 + -3

Combine like terms: 10 + -3 = 7
-36n = 7

Divide each side by '-36'.
n = -0.1944444444

Simplifying
n = -0.1944444444