-2v(v+2)=3v-9+2(5v+7)

Solution for -2v(v+2)=3v-9+2(5v+7) equation:

Simplifying
-2v(v + 2) = 3v + -9 + 2(5v + 7)

Reorder the terms:
-2v(2 + v) = 3v + -9 + 2(5v + 7)
(2 * -2v + v * -2v) = 3v + -9 + 2(5v + 7)
(-4v + -2v2) = 3v + -9 + 2(5v + 7)

Reorder the terms:
-4v + -2v2 = 3v + -9 + 2(7 + 5v)
-4v + -2v2 = 3v + -9 + (7 * 2 + 5v * 2)
-4v + -2v2 = 3v + -9 + (14 + 10v)

Reorder the terms:
-4v + -2v2 = -9 + 14 + 3v + 10v

Combine like terms: -9 + 14 = 5
-4v + -2v2 = 5 + 3v + 10v

Combine like terms: 3v + 10v = 13v
-4v + -2v2 = 5 + 13v

Solving
-4v + -2v2 = 5 + 13v

Solving for variable 'v'.

Reorder the terms:
-5 + -4v + -13v + -2v2 = 5 + 13v + -5 + -13v

Combine like terms: -4v + -13v = -17v
-5 + -17v + -2v2 = 5 + 13v + -5 + -13v

Reorder the terms:
-5 + -17v + -2v2 = 5 + -5 + 13v + -13v

Combine like terms: 5 + -5 = 0
-5 + -17v + -2v2 = 0 + 13v + -13v
-5 + -17v + -2v2 = 13v + -13v

Combine like terms: 13v + -13v = 0
-5 + -17v + -2v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 17v + 2v2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 17v + 2v2)' equal to zero and attempt to solve:

Simplifying
5 + 17v + 2v2 = 0

Solving
5 + 17v + 2v2 = 0

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

Divide each side by '2'.
2.5 + 8.5v + v2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 8.5v + -2.5 + v2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 8.5v + v2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 8.5v + v2 = 0 + -2.5
8.5v + v2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
8.5v + v2 = -2.5

The v term is 8.5v.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5v + 18.0625 + v2 = -2.5 + 18.0625

Reorder the terms:
18.0625 + 8.5v + v2 = -2.5 + 18.0625

Combine like terms: -2.5 + 18.0625 = 15.5625
18.0625 + 8.5v + v2 = 15.5625

Factor a perfect square on the left side:
(v + 4.25)(v + 4.25) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(v + 4.25) equal to 3.94493346 and -3.94493346.

Subproblem 1
v + 4.25 = 3.94493346

Simplifying
v + 4.25 = 3.94493346

Reorder the terms:
4.25 + v = 3.94493346

Solving
4.25 + v = 3.94493346

Solving for variable 'v'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + v = 3.94493346 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + v = 3.94493346 + -4.25
v = 3.94493346 + -4.25

Combine like terms: 3.94493346 + -4.25 = -0.30506654
v = -0.30506654

Simplifying
v = -0.30506654

Subproblem 2
v + 4.25 = -3.94493346

Simplifying
v + 4.25 = -3.94493346

Reorder the terms:
4.25 + v = -3.94493346

Solving
4.25 + v = -3.94493346

Solving for variable 'v'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + v = -3.94493346 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + v = -3.94493346 + -4.25
v = -3.94493346 + -4.25

Combine like terms: -3.94493346 + -4.25 = -8.19493346
v = -8.19493346

Simplifying
v = -8.19493346

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.30506654, -8.19493346}
Solution
v = {-0.30506654, -8.19493346}