n+3+9=3(n-2)-12(n-4)

Solution for n+3+9=3(n-2)-12(n-4) equation:

Simplifying
n + 3 + 9 = 3(n + -2) + -12(n + -4)

Reorder the terms:
3 + 9 + n = 3(n + -2) + -12(n + -4)

Combine like terms: 3 + 9 = 12
12 + n = 3(n + -2) + -12(n + -4)

Reorder the terms:
12 + n = 3(-2 + n) + -12(n + -4)
12 + n = (-2 * 3 + n * 3) + -12(n + -4)
12 + n = (-6 + 3n) + -12(n + -4)

Reorder the terms:
12 + n = -6 + 3n + -12(-4 + n)
12 + n = -6 + 3n + (-4 * -12 + n * -12)
12 + n = -6 + 3n + (48 + -12n)

Reorder the terms:
12 + n = -6 + 48 + 3n + -12n

Combine like terms: -6 + 48 = 42
12 + n = 42 + 3n + -12n

Combine like terms: 3n + -12n = -9n
12 + n = 42 + -9n

Solving
12 + n = 42 + -9n

Solving for variable 'n'.

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

Add '9n' to each side of the equation.
12 + n + 9n = 42 + -9n + 9n

Combine like terms: n + 9n = 10n
12 + 10n = 42 + -9n + 9n

Combine like terms: -9n + 9n = 0
12 + 10n = 42 + 0
12 + 10n = 42

Add '-12' to each side of the equation.
12 + -12 + 10n = 42 + -12

Combine like terms: 12 + -12 = 0
0 + 10n = 42 + -12
10n = 42 + -12

Combine like terms: 42 + -12 = 30
10n = 30

Divide each side by '10'.
n = 3

Simplifying
n = 3