2(2n+3)=7(5n+6)+1

Solution for 2(2n+3)=7(5n+6)+1 equation:

Simplifying
2(2n + 3) = 7(5n + 6) + 1

Reorder the terms:
2(3 + 2n) = 7(5n + 6) + 1
(3 * 2 + 2n * 2) = 7(5n + 6) + 1
(6 + 4n) = 7(5n + 6) + 1

Reorder the terms:
6 + 4n = 7(6 + 5n) + 1
6 + 4n = (6 * 7 + 5n * 7) + 1
6 + 4n = (42 + 35n) + 1

Reorder the terms:
6 + 4n = 42 + 1 + 35n

Combine like terms: 42 + 1 = 43
6 + 4n = 43 + 35n

Solving
6 + 4n = 43 + 35n

Solving for variable 'n'.

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

Add '-35n' to each side of the equation.
6 + 4n + -35n = 43 + 35n + -35n

Combine like terms: 4n + -35n = -31n
6 + -31n = 43 + 35n + -35n

Combine like terms: 35n + -35n = 0
6 + -31n = 43 + 0
6 + -31n = 43

Add '-6' to each side of the equation.
6 + -6 + -31n = 43 + -6

Combine like terms: 6 + -6 = 0
0 + -31n = 43 + -6
-31n = 43 + -6

Combine like terms: 43 + -6 = 37
-31n = 37

Divide each side by '-31'.
n = -1.193548387

Simplifying
n = -1.193548387