-4=-1-3v(2v+3)

Solution for -4=-1-3v(2v+3) equation:

Simplifying
-4 = -1 + -3v(2v + 3)

Reorder the terms:
-4 = -1 + -3v(3 + 2v)
-4 = -1 + (3 * -3v + 2v * -3v)
-4 = -1 + (-9v + -6v2)

Solving
-4 = -1 + -9v + -6v2

Solving for variable 'v'.

Combine like terms: -4 + 1 = -3
-3 + 9v + 6v2 = -1 + -9v + -6v2 + 1 + 9v + 6v2

Reorder the terms:
-3 + 9v + 6v2 = -1 + 1 + -9v + 9v + -6v2 + 6v2

Combine like terms: -1 + 1 = 0
-3 + 9v + 6v2 = 0 + -9v + 9v + -6v2 + 6v2
-3 + 9v + 6v2 = -9v + 9v + -6v2 + 6v2

Combine like terms: -9v + 9v = 0
-3 + 9v + 6v2 = 0 + -6v2 + 6v2
-3 + 9v + 6v2 = -6v2 + 6v2

Combine like terms: -6v2 + 6v2 = 0
-3 + 9v + 6v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 3v + 2v2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 3v + 2v2)' equal to zero and attempt to solve:

Simplifying
-1 + 3v + 2v2 = 0

Solving
-1 + 3v + 2v2 = 0

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

Divide each side by '2'.
-0.5 + 1.5v + v2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.5v + 0.5 + v2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.5v + v2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.5v + v2 = 0 + 0.5
1.5v + v2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.5v + v2 = 0.5

The v term is 1.5v.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5v + 0.5625 + v2 = 0.5 + 0.5625

Reorder the terms:
0.5625 + 1.5v + v2 = 0.5 + 0.5625

Combine like terms: 0.5 + 0.5625 = 1.0625
0.5625 + 1.5v + v2 = 1.0625

Factor a perfect square on the left side:
(v + 0.75)(v + 0.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(v + 0.75) equal to 1.030776406 and -1.030776406.

Subproblem 1
v + 0.75 = 1.030776406

Simplifying
v + 0.75 = 1.030776406

Reorder the terms:
0.75 + v = 1.030776406

Solving
0.75 + v = 1.030776406

Solving for variable 'v'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + v = 1.030776406 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + v = 1.030776406 + -0.75
v = 1.030776406 + -0.75

Combine like terms: 1.030776406 + -0.75 = 0.280776406
v = 0.280776406

Simplifying
v = 0.280776406

Subproblem 2
v + 0.75 = -1.030776406

Simplifying
v + 0.75 = -1.030776406

Reorder the terms:
0.75 + v = -1.030776406

Solving
0.75 + v = -1.030776406

Solving for variable 'v'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + v = -1.030776406 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + v = -1.030776406 + -0.75
v = -1.030776406 + -0.75

Combine like terms: -1.030776406 + -0.75 = -1.780776406
v = -1.780776406

Simplifying
v = -1.780776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.280776406, -1.780776406}
Solution
v = {0.280776406, -1.780776406}