2(2n+3)=9(5n+1)+2

Solution for 2(2n+3)=9(5n+1)+2 equation:

Simplifying
2(2n + 3) = 9(5n + 1) + 2

Reorder the terms:
2(3 + 2n) = 9(5n + 1) + 2
(3 * 2 + 2n * 2) = 9(5n + 1) + 2
(6 + 4n) = 9(5n + 1) + 2

Reorder the terms:
6 + 4n = 9(1 + 5n) + 2
6 + 4n = (1 * 9 + 5n * 9) + 2
6 + 4n = (9 + 45n) + 2

Reorder the terms:
6 + 4n = 9 + 2 + 45n

Combine like terms: 9 + 2 = 11
6 + 4n = 11 + 45n

Solving
6 + 4n = 11 + 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.
6 + 4n + -45n = 11 + 45n + -45n

Combine like terms: 4n + -45n = -41n
6 + -41n = 11 + 45n + -45n

Combine like terms: 45n + -45n = 0
6 + -41n = 11 + 0
6 + -41n = 11

Add '-6' to each side of the equation.
6 + -6 + -41n = 11 + -6

Combine like terms: 6 + -6 = 0
0 + -41n = 11 + -6
-41n = 11 + -6

Combine like terms: 11 + -6 = 5
-41n = 5

Divide each side by '-41'.
n = -0.1219512195

Simplifying
n = -0.1219512195