(5v+3)(4+v)=3

Solution for (5v+3)(4+v)=3 equation:

Simplifying
(5v + 3)(4 + v) = 3

Reorder the terms:
(3 + 5v)(4 + v) = 3

Multiply (3 + 5v) * (4 + v)
(3(4 + v) + 5v * (4 + v)) = 3
((4 * 3 + v * 3) + 5v * (4 + v)) = 3
((12 + 3v) + 5v * (4 + v)) = 3
(12 + 3v + (4 * 5v + v * 5v)) = 3
(12 + 3v + (20v + 5v2)) = 3

Combine like terms: 3v + 20v = 23v
(12 + 23v + 5v2) = 3

Solving
12 + 23v + 5v2 = 3

Solving for variable 'v'.

Reorder the terms:
12 + -3 + 23v + 5v2 = 3 + -3

Combine like terms: 12 + -3 = 9
9 + 23v + 5v2 = 3 + -3

Combine like terms: 3 + -3 = 0
9 + 23v + 5v2 = 0

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

Divide each side by '5'.
1.8 + 4.6v + v2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + 4.6v + -1.8 + v2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + 4.6v + v2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + 4.6v + v2 = 0 + -1.8
4.6v + v2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
4.6v + v2 = -1.8

The v term is 4.6v.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6v + 5.29 + v2 = -1.8 + 5.29

Reorder the terms:
5.29 + 4.6v + v2 = -1.8 + 5.29

Combine like terms: -1.8 + 5.29 = 3.49
5.29 + 4.6v + v2 = 3.49

Factor a perfect square on the left side:
(v + 2.3)(v + 2.3) = 3.49

Calculate the square root of the right side: 1.868154169

Break this problem into two subproblems by setting 
(v + 2.3) equal to 1.868154169 and -1.868154169.

Subproblem 1
v + 2.3 = 1.868154169

Simplifying
v + 2.3 = 1.868154169

Reorder the terms:
2.3 + v = 1.868154169

Solving
2.3 + v = 1.868154169

Solving for variable 'v'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + v = 1.868154169 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + v = 1.868154169 + -2.3
v = 1.868154169 + -2.3

Combine like terms: 1.868154169 + -2.3 = -0.431845831
v = -0.431845831

Simplifying
v = -0.431845831

Subproblem 2
v + 2.3 = -1.868154169

Simplifying
v + 2.3 = -1.868154169

Reorder the terms:
2.3 + v = -1.868154169

Solving
2.3 + v = -1.868154169

Solving for variable 'v'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + v = -1.868154169 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + v = -1.868154169 + -2.3
v = -1.868154169 + -2.3

Combine like terms: -1.868154169 + -2.3 = -4.168154169
v = -4.168154169

Simplifying
v = -4.168154169

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.431845831, -4.168154169}