2(v+3)+8v=5(3v+3)+1

Solution for 2(v+3)+8v=5(3v+3)+1 equation:

Simplifying
2(v + 3) + 8v = 5(3v + 3) + 1

Reorder the terms:
2(3 + v) + 8v = 5(3v + 3) + 1
(3 * 2 + v * 2) + 8v = 5(3v + 3) + 1
(6 + 2v) + 8v = 5(3v + 3) + 1

Combine like terms: 2v + 8v = 10v
6 + 10v = 5(3v + 3) + 1

Reorder the terms:
6 + 10v = 5(3 + 3v) + 1
6 + 10v = (3 * 5 + 3v * 5) + 1
6 + 10v = (15 + 15v) + 1

Reorder the terms:
6 + 10v = 15 + 1 + 15v

Combine like terms: 15 + 1 = 16
6 + 10v = 16 + 15v

Solving
6 + 10v = 16 + 15v

Solving for variable 'v'.

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

Add '-15v' to each side of the equation.
6 + 10v + -15v = 16 + 15v + -15v

Combine like terms: 10v + -15v = -5v
6 + -5v = 16 + 15v + -15v

Combine like terms: 15v + -15v = 0
6 + -5v = 16 + 0
6 + -5v = 16

Add '-6' to each side of the equation.
6 + -6 + -5v = 16 + -6

Combine like terms: 6 + -6 = 0
0 + -5v = 16 + -6
-5v = 16 + -6

Combine like terms: 16 + -6 = 10
-5v = 10

Divide each side by '-5'.
v = -2

Simplifying
v = -2