2(2n+3)+13=3(2n+1)

Solution for 2(2n+3)+13=3(2n+1) equation:

Simplifying
2(2n + 3) + 13 = 3(2n + 1)

Reorder the terms:
2(3 + 2n) + 13 = 3(2n + 1)
(3 * 2 + 2n * 2) + 13 = 3(2n + 1)
(6 + 4n) + 13 = 3(2n + 1)

Reorder the terms:
6 + 13 + 4n = 3(2n + 1)

Combine like terms: 6 + 13 = 19
19 + 4n = 3(2n + 1)

Reorder the terms:
19 + 4n = 3(1 + 2n)
19 + 4n = (1 * 3 + 2n * 3)
19 + 4n = (3 + 6n)

Solving
19 + 4n = 3 + 6n

Solving for variable 'n'.

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

Add '-6n' to each side of the equation.
19 + 4n + -6n = 3 + 6n + -6n

Combine like terms: 4n + -6n = -2n
19 + -2n = 3 + 6n + -6n

Combine like terms: 6n + -6n = 0
19 + -2n = 3 + 0
19 + -2n = 3

Add '-19' to each side of the equation.
19 + -19 + -2n = 3 + -19

Combine like terms: 19 + -19 = 0
0 + -2n = 3 + -19
-2n = 3 + -19

Combine like terms: 3 + -19 = -16
-2n = -16

Divide each side by '-2'.
n = 8

Simplifying
n = 8