-8(v+4)4v+7=5v+8

Solution for -8(v+4)4v+7=5v+8 equation:

Simplifying
-8(v + 4) * 4v + 7 = 5v + 8

Reorder the terms:
-8(4 + v) * 4v + 7 = 5v + 8

Reorder the terms for easier multiplication:
-8 * 4v(4 + v) + 7 = 5v + 8

Multiply -8 * 4
-32v(4 + v) + 7 = 5v + 8
(4 * -32v + v * -32v) + 7 = 5v + 8
(-128v + -32v2) + 7 = 5v + 8

Reorder the terms:
7 + -128v + -32v2 = 5v + 8

Reorder the terms:
7 + -128v + -32v2 = 8 + 5v

Solving
7 + -128v + -32v2 = 8 + 5v

Solving for variable 'v'.

Reorder the terms:
7 + -8 + -128v + -5v + -32v2 = 8 + 5v + -8 + -5v

Combine like terms: 7 + -8 = -1
-1 + -128v + -5v + -32v2 = 8 + 5v + -8 + -5v

Combine like terms: -128v + -5v = -133v
-1 + -133v + -32v2 = 8 + 5v + -8 + -5v

Reorder the terms:
-1 + -133v + -32v2 = 8 + -8 + 5v + -5v

Combine like terms: 8 + -8 = 0
-1 + -133v + -32v2 = 0 + 5v + -5v
-1 + -133v + -32v2 = 5v + -5v

Combine like terms: 5v + -5v = 0
-1 + -133v + -32v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 133v + 32v2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 133v + 32v2)' equal to zero and attempt to solve:

Simplifying
1 + 133v + 32v2 = 0

Solving
1 + 133v + 32v2 = 0

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

Divide each side by '32'.
0.03125 + 4.15625v + v2 = 0

Move the constant term to the right:

Add '-0.03125' to each side of the equation.
0.03125 + 4.15625v + -0.03125 + v2 = 0 + -0.03125

Reorder the terms:
0.03125 + -0.03125 + 4.15625v + v2 = 0 + -0.03125

Combine like terms: 0.03125 + -0.03125 = 0.00000
0.00000 + 4.15625v + v2 = 0 + -0.03125
4.15625v + v2 = 0 + -0.03125

Combine like terms: 0 + -0.03125 = -0.03125
4.15625v + v2 = -0.03125

The v term is 4.15625v.  Take half its coefficient (2.078125).
Square it (4.318603516) and add it to both sides.

Add '4.318603516' to each side of the equation.
4.15625v + 4.318603516 + v2 = -0.03125 + 4.318603516

Reorder the terms:
4.318603516 + 4.15625v + v2 = -0.03125 + 4.318603516

Combine like terms: -0.03125 + 4.318603516 = 4.287353516
4.318603516 + 4.15625v + v2 = 4.287353516

Factor a perfect square on the left side:
(v + 2.078125)(v + 2.078125) = 4.287353516

Calculate the square root of the right side: 2.070592552

Break this problem into two subproblems by setting 
(v + 2.078125) equal to 2.070592552 and -2.070592552.

Subproblem 1
v + 2.078125 = 2.070592552

Simplifying
v + 2.078125 = 2.070592552

Reorder the terms:
2.078125 + v = 2.070592552

Solving
2.078125 + v = 2.070592552

Solving for variable 'v'.

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

Add '-2.078125' to each side of the equation.
2.078125 + -2.078125 + v = 2.070592552 + -2.078125

Combine like terms: 2.078125 + -2.078125 = 0.000000
0.000000 + v = 2.070592552 + -2.078125
v = 2.070592552 + -2.078125

Combine like terms: 2.070592552 + -2.078125 = -0.007532448
v = -0.007532448

Simplifying
v = -0.007532448

Subproblem 2
v + 2.078125 = -2.070592552

Simplifying
v + 2.078125 = -2.070592552

Reorder the terms:
2.078125 + v = -2.070592552

Solving
2.078125 + v = -2.070592552

Solving for variable 'v'.

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

Add '-2.078125' to each side of the equation.
2.078125 + -2.078125 + v = -2.070592552 + -2.078125

Combine like terms: 2.078125 + -2.078125 = 0.000000
0.000000 + v = -2.070592552 + -2.078125
v = -2.070592552 + -2.078125

Combine like terms: -2.070592552 + -2.078125 = -4.148717552
v = -4.148717552

Simplifying
v = -4.148717552

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.007532448, -4.148717552}
Solution
v = {-0.007532448, -4.148717552}