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

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

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

Reorder the terms:
7(6 + n) = 3(n + -2)
(6 * 7 + n * 7) = 3(n + -2)
(42 + 7n) = 3(n + -2)

Reorder the terms:
42 + 7n = 3(-2 + n)
42 + 7n = (-2 * 3 + n * 3)
42 + 7n = (-6 + 3n)

Solving
42 + 7n = -6 + 3n

Solving for variable 'n'.

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

Add '-3n' to each side of the equation.
42 + 7n + -3n = -6 + 3n + -3n

Combine like terms: 7n + -3n = 4n
42 + 4n = -6 + 3n + -3n

Combine like terms: 3n + -3n = 0
42 + 4n = -6 + 0
42 + 4n = -6

Add '-42' to each side of the equation.
42 + -42 + 4n = -6 + -42

Combine like terms: 42 + -42 = 0
0 + 4n = -6 + -42
4n = -6 + -42

Combine like terms: -6 + -42 = -48
4n = -48

Divide each side by '4'.
n = -12

Simplifying
n = -12