2v+18=16-4v(v+2)

Solution for 2v+18=16-4v(v+2) equation:

Simplifying
2v + 18 = 16 + -4v(v + 2)

Reorder the terms:
18 + 2v = 16 + -4v(v + 2)

Reorder the terms:
18 + 2v = 16 + -4v(2 + v)
18 + 2v = 16 + (2 * -4v + v * -4v)
18 + 2v = 16 + (-8v + -4v2)

Solving
18 + 2v = 16 + -8v + -4v2

Solving for variable 'v'.

Reorder the terms:
18 + -16 + 2v + 8v + 4v2 = 16 + -8v + -4v2 + -16 + 8v + 4v2

Combine like terms: 18 + -16 = 2
2 + 2v + 8v + 4v2 = 16 + -8v + -4v2 + -16 + 8v + 4v2

Combine like terms: 2v + 8v = 10v
2 + 10v + 4v2 = 16 + -8v + -4v2 + -16 + 8v + 4v2

Reorder the terms:
2 + 10v + 4v2 = 16 + -16 + -8v + 8v + -4v2 + 4v2

Combine like terms: 16 + -16 = 0
2 + 10v + 4v2 = 0 + -8v + 8v + -4v2 + 4v2
2 + 10v + 4v2 = -8v + 8v + -4v2 + 4v2

Combine like terms: -8v + 8v = 0
2 + 10v + 4v2 = 0 + -4v2 + 4v2
2 + 10v + 4v2 = -4v2 + 4v2

Combine like terms: -4v2 + 4v2 = 0
2 + 10v + 4v2 = 0

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

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

Simplifying
1 + 5v + 2v2 = 0

Solving
1 + 5v + 2v2 = 0

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

Divide each side by '2'.
0.5 + 2.5v + v2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.5v + -0.5 + v2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.5v + v2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.5v + v2 = 0 + -0.5
2.5v + v2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.5v + v2 = -0.5

The v term is 2.5v.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5v + 1.5625 + v2 = -0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5v + v2 = -0.5 + 1.5625

Combine like terms: -0.5 + 1.5625 = 1.0625
1.5625 + 2.5v + v2 = 1.0625

Factor a perfect square on the left side:
(v + 1.25)(v + 1.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(v + 1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
v + 1.25 = 1.030776406

Simplifying
v + 1.25 = 1.030776406

Reorder the terms:
1.25 + v = 1.030776406

Solving
1.25 + v = 1.030776406

Solving for variable 'v'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + v = 1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + v = 1.030776406 + -1.25
v = 1.030776406 + -1.25

Combine like terms: 1.030776406 + -1.25 = -0.219223594
v = -0.219223594

Simplifying
v = -0.219223594

Subproblem 2
v + 1.25 = -1.030776406

Simplifying
v + 1.25 = -1.030776406

Reorder the terms:
1.25 + v = -1.030776406

Solving
1.25 + v = -1.030776406

Solving for variable 'v'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + v = -1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + v = -1.030776406 + -1.25
v = -1.030776406 + -1.25

Combine like terms: -1.030776406 + -1.25 = -2.280776406
v = -2.280776406

Simplifying
v = -2.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.219223594, -2.280776406}
Solution
v = {-0.219223594, -2.280776406}