3(n+2)=15-6(n-3)

Solution for 3(n+2)=15-6(n-3) equation:

Simplifying
3(n + 2) = 15 + -6(n + -3)

Reorder the terms:
3(2 + n) = 15 + -6(n + -3)
(2 * 3 + n * 3) = 15 + -6(n + -3)
(6 + 3n) = 15 + -6(n + -3)

Reorder the terms:
6 + 3n = 15 + -6(-3 + n)
6 + 3n = 15 + (-3 * -6 + n * -6)
6 + 3n = 15 + (18 + -6n)

Combine like terms: 15 + 18 = 33
6 + 3n = 33 + -6n

Solving
6 + 3n = 33 + -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.
6 + 3n + 6n = 33 + -6n + 6n

Combine like terms: 3n + 6n = 9n
6 + 9n = 33 + -6n + 6n

Combine like terms: -6n + 6n = 0
6 + 9n = 33 + 0
6 + 9n = 33

Add '-6' to each side of the equation.
6 + -6 + 9n = 33 + -6

Combine like terms: 6 + -6 = 0
0 + 9n = 33 + -6
9n = 33 + -6

Combine like terms: 33 + -6 = 27
9n = 27

Divide each side by '9'.
n = 3

Simplifying
n = 3