-17=6(v+8)7v

Solution for -17=6(v+8)7v equation:

Simplifying
-17 = 6(v + 8) * 7v

Reorder the terms:
-17 = 6(8 + v) * 7v

Reorder the terms for easier multiplication:
-17 = 6 * 7v(8 + v)

Multiply 6 * 7
-17 = 42v(8 + v)
-17 = (8 * 42v + v * 42v)
-17 = (336v + 42v2)

Solving
-17 = 336v + 42v2

Solving for variable 'v'.

Reorder the terms:
-17 + -336v + -42v2 = 336v + -336v + 42v2 + -42v2

Combine like terms: 336v + -336v = 0
-17 + -336v + -42v2 = 0 + 42v2 + -42v2
-17 + -336v + -42v2 = 42v2 + -42v2

Combine like terms: 42v2 + -42v2 = 0
-17 + -336v + -42v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 336v + 42v2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(17 + 336v + 42v2)' equal to zero and attempt to solve:

Simplifying
17 + 336v + 42v2 = 0

Solving
17 + 336v + 42v2 = 0

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

Divide each side by '42'.
0.4047619048 + 8v + v2 = 0

Move the constant term to the right:

Add '-0.4047619048' to each side of the equation.
0.4047619048 + 8v + -0.4047619048 + v2 = 0 + -0.4047619048

Reorder the terms:
0.4047619048 + -0.4047619048 + 8v + v2 = 0 + -0.4047619048

Combine like terms: 0.4047619048 + -0.4047619048 = 0.0000000000
0.0000000000 + 8v + v2 = 0 + -0.4047619048
8v + v2 = 0 + -0.4047619048

Combine like terms: 0 + -0.4047619048 = -0.4047619048
8v + v2 = -0.4047619048

The v term is 8v.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8v + 16 + v2 = -0.4047619048 + 16

Reorder the terms:
16 + 8v + v2 = -0.4047619048 + 16

Combine like terms: -0.4047619048 + 16 = 15.5952380952
16 + 8v + v2 = 15.5952380952

Factor a perfect square on the left side:
(v + 4)(v + 4) = 15.5952380952

Calculate the square root of the right side: 3.949080665

Break this problem into two subproblems by setting 
(v + 4) equal to 3.949080665 and -3.949080665.

Subproblem 1
v + 4 = 3.949080665

Simplifying
v + 4 = 3.949080665

Reorder the terms:
4 + v = 3.949080665

Solving
4 + v = 3.949080665

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = 3.949080665 + -4

Combine like terms: 4 + -4 = 0
0 + v = 3.949080665 + -4
v = 3.949080665 + -4

Combine like terms: 3.949080665 + -4 = -0.050919335
v = -0.050919335

Simplifying
v = -0.050919335

Subproblem 2
v + 4 = -3.949080665

Simplifying
v + 4 = -3.949080665

Reorder the terms:
4 + v = -3.949080665

Solving
4 + v = -3.949080665

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = -3.949080665 + -4

Combine like terms: 4 + -4 = 0
0 + v = -3.949080665 + -4
v = -3.949080665 + -4

Combine like terms: -3.949080665 + -4 = -7.949080665
v = -7.949080665

Simplifying
v = -7.949080665

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.050919335, -7.949080665}
Solution
v = {-0.050919335, -7.949080665}