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

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

Simplifying
2(3 + 5n) = 5(3n + 9)
(3 * 2 + 5n * 2) = 5(3n + 9)
(6 + 10n) = 5(3n + 9)

Reorder the terms:
6 + 10n = 5(9 + 3n)
6 + 10n = (9 * 5 + 3n * 5)
6 + 10n = (45 + 15n)

Solving
6 + 10n = 45 + 15n

Solving for variable 'n'.

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

Add '-15n' to each side of the equation.
6 + 10n + -15n = 45 + 15n + -15n

Combine like terms: 10n + -15n = -5n
6 + -5n = 45 + 15n + -15n

Combine like terms: 15n + -15n = 0
6 + -5n = 45 + 0
6 + -5n = 45

Add '-6' to each side of the equation.
6 + -6 + -5n = 45 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 45 + -6
-5n = 45 + -6

Combine like terms: 45 + -6 = 39
-5n = 39

Divide each side by '-5'.
n = -7.8

Simplifying
n = -7.8