-7(2v+8)=-(1+6v)3v

Solution for -7(2v+8)=-(1+6v)3v equation:

Simplifying
-7(2v + 8) = -1(1 + 6v) * 3v

Reorder the terms:
-7(8 + 2v) = -1(1 + 6v) * 3v
(8 * -7 + 2v * -7) = -1(1 + 6v) * 3v
(-56 + -14v) = -1(1 + 6v) * 3v

Reorder the terms for easier multiplication:
-56 + -14v = -1 * 3v(1 + 6v)

Multiply -1 * 3
-56 + -14v = -3v(1 + 6v)
-56 + -14v = (1 * -3v + 6v * -3v)
-56 + -14v = (-3v + -18v2)

Solving
-56 + -14v = -3v + -18v2

Solving for variable 'v'.

Combine like terms: -14v + 3v = -11v
-56 + -11v + 18v2 = -3v + -18v2 + 3v + 18v2

Reorder the terms:
-56 + -11v + 18v2 = -3v + 3v + -18v2 + 18v2

Combine like terms: -3v + 3v = 0
-56 + -11v + 18v2 = 0 + -18v2 + 18v2
-56 + -11v + 18v2 = -18v2 + 18v2

Combine like terms: -18v2 + 18v2 = 0
-56 + -11v + 18v2 = 0

Begin completing the square.  Divide all terms by
18 the coefficient of the squared term: 

Divide each side by '18'.
-3.111111111 + -0.6111111111v + v2 = 0

Move the constant term to the right:

Add '3.111111111' to each side of the equation.
-3.111111111 + -0.6111111111v + 3.111111111 + v2 = 0 + 3.111111111

Reorder the terms:
-3.111111111 + 3.111111111 + -0.6111111111v + v2 = 0 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + -0.6111111111v + v2 = 0 + 3.111111111
-0.6111111111v + v2 = 0 + 3.111111111

Combine like terms: 0 + 3.111111111 = 3.111111111
-0.6111111111v + v2 = 3.111111111

The v term is -0.6111111111v.  Take half its coefficient (-0.3055555556).
Square it (0.09336419756) and add it to both sides.

Add '0.09336419756' to each side of the equation.
-0.6111111111v + 0.09336419756 + v2 = 3.111111111 + 0.09336419756

Reorder the terms:
0.09336419756 + -0.6111111111v + v2 = 3.111111111 + 0.09336419756

Combine like terms: 3.111111111 + 0.09336419756 = 3.20447530856
0.09336419756 + -0.6111111111v + v2 = 3.20447530856

Factor a perfect square on the left side:
(v + -0.3055555556)(v + -0.3055555556) = 3.20447530856

Calculate the square root of the right side: 1.790104832

Break this problem into two subproblems by setting 
(v + -0.3055555556) equal to 1.790104832 and -1.790104832.

Subproblem 1
v + -0.3055555556 = 1.790104832

Simplifying
v + -0.3055555556 = 1.790104832

Reorder the terms:
-0.3055555556 + v = 1.790104832

Solving
-0.3055555556 + v = 1.790104832

Solving for variable 'v'.

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

Add '0.3055555556' to each side of the equation.
-0.3055555556 + 0.3055555556 + v = 1.790104832 + 0.3055555556

Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000
0.0000000000 + v = 1.790104832 + 0.3055555556
v = 1.790104832 + 0.3055555556

Combine like terms: 1.790104832 + 0.3055555556 = 2.0956603876
v = 2.0956603876

Simplifying
v = 2.0956603876

Subproblem 2
v + -0.3055555556 = -1.790104832

Simplifying
v + -0.3055555556 = -1.790104832

Reorder the terms:
-0.3055555556 + v = -1.790104832

Solving
-0.3055555556 + v = -1.790104832

Solving for variable 'v'.

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

Add '0.3055555556' to each side of the equation.
-0.3055555556 + 0.3055555556 + v = -1.790104832 + 0.3055555556

Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000
0.0000000000 + v = -1.790104832 + 0.3055555556
v = -1.790104832 + 0.3055555556

Combine like terms: -1.790104832 + 0.3055555556 = -1.4845492764
v = -1.4845492764

Simplifying
v = -1.4845492764

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.0956603876, -1.4845492764}