1-5n+3n+4=-3(n+8)+2(6n-2)

Solution for 1-5n+3n+4=-3(n+8)+2(6n-2) equation:

Simplifying
1 + -5n + 3n + 4 = -3(n + 8) + 2(6n + -2)

Reorder the terms:
1 + 4 + -5n + 3n = -3(n + 8) + 2(6n + -2)

Combine like terms: 1 + 4 = 5
5 + -5n + 3n = -3(n + 8) + 2(6n + -2)

Combine like terms: -5n + 3n = -2n
5 + -2n = -3(n + 8) + 2(6n + -2)

Reorder the terms:
5 + -2n = -3(8 + n) + 2(6n + -2)
5 + -2n = (8 * -3 + n * -3) + 2(6n + -2)
5 + -2n = (-24 + -3n) + 2(6n + -2)

Reorder the terms:
5 + -2n = -24 + -3n + 2(-2 + 6n)
5 + -2n = -24 + -3n + (-2 * 2 + 6n * 2)
5 + -2n = -24 + -3n + (-4 + 12n)

Reorder the terms:
5 + -2n = -24 + -4 + -3n + 12n

Combine like terms: -24 + -4 = -28
5 + -2n = -28 + -3n + 12n

Combine like terms: -3n + 12n = 9n
5 + -2n = -28 + 9n

Solving
5 + -2n = -28 + 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.
5 + -2n + -9n = -28 + 9n + -9n

Combine like terms: -2n + -9n = -11n
5 + -11n = -28 + 9n + -9n

Combine like terms: 9n + -9n = 0
5 + -11n = -28 + 0
5 + -11n = -28

Add '-5' to each side of the equation.
5 + -5 + -11n = -28 + -5

Combine like terms: 5 + -5 = 0
0 + -11n = -28 + -5
-11n = -28 + -5

Combine like terms: -28 + -5 = -33
-11n = -33

Divide each side by '-11'.
n = 3

Simplifying
n = 3