7(n-2)=2(n+3)+3(n-4)

Solution for 7(n-2)=2(n+3)+3(n-4) equation:

Simplifying
7(n + -2) = 2(n + 3) + 3(n + -4)

Reorder the terms:
7(-2 + n) = 2(n + 3) + 3(n + -4)
(-2 * 7 + n * 7) = 2(n + 3) + 3(n + -4)
(-14 + 7n) = 2(n + 3) + 3(n + -4)

Reorder the terms:
-14 + 7n = 2(3 + n) + 3(n + -4)
-14 + 7n = (3 * 2 + n * 2) + 3(n + -4)
-14 + 7n = (6 + 2n) + 3(n + -4)

Reorder the terms:
-14 + 7n = 6 + 2n + 3(-4 + n)
-14 + 7n = 6 + 2n + (-4 * 3 + n * 3)
-14 + 7n = 6 + 2n + (-12 + 3n)

Reorder the terms:
-14 + 7n = 6 + -12 + 2n + 3n

Combine like terms: 6 + -12 = -6
-14 + 7n = -6 + 2n + 3n

Combine like terms: 2n + 3n = 5n
-14 + 7n = -6 + 5n

Solving
-14 + 7n = -6 + 5n

Solving for variable 'n'.

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

Add '-5n' to each side of the equation.
-14 + 7n + -5n = -6 + 5n + -5n

Combine like terms: 7n + -5n = 2n
-14 + 2n = -6 + 5n + -5n

Combine like terms: 5n + -5n = 0
-14 + 2n = -6 + 0
-14 + 2n = -6

Add '14' to each side of the equation.
-14 + 14 + 2n = -6 + 14

Combine like terms: -14 + 14 = 0
0 + 2n = -6 + 14
2n = -6 + 14

Combine like terms: -6 + 14 = 8
2n = 8

Divide each side by '2'.
n = 4

Simplifying
n = 4