-9v(v+3)+2v+7=7v+12

Solution for -9v(v+3)+2v+7=7v+12 equation:

Simplifying
-9v(v + 3) + 2v + 7 = 7v + 12

Reorder the terms:
-9v(3 + v) + 2v + 7 = 7v + 12
(3 * -9v + v * -9v) + 2v + 7 = 7v + 12
(-27v + -9v2) + 2v + 7 = 7v + 12

Reorder the terms:
7 + -27v + 2v + -9v2 = 7v + 12

Combine like terms: -27v + 2v = -25v
7 + -25v + -9v2 = 7v + 12

Reorder the terms:
7 + -25v + -9v2 = 12 + 7v

Solving
7 + -25v + -9v2 = 12 + 7v

Solving for variable 'v'.

Reorder the terms:
7 + -12 + -25v + -7v + -9v2 = 12 + 7v + -12 + -7v

Combine like terms: 7 + -12 = -5
-5 + -25v + -7v + -9v2 = 12 + 7v + -12 + -7v

Combine like terms: -25v + -7v = -32v
-5 + -32v + -9v2 = 12 + 7v + -12 + -7v

Reorder the terms:
-5 + -32v + -9v2 = 12 + -12 + 7v + -7v

Combine like terms: 12 + -12 = 0
-5 + -32v + -9v2 = 0 + 7v + -7v
-5 + -32v + -9v2 = 7v + -7v

Combine like terms: 7v + -7v = 0
-5 + -32v + -9v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 32v + 9v2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 32v + 9v2)' equal to zero and attempt to solve:

Simplifying
5 + 32v + 9v2 = 0

Solving
5 + 32v + 9v2 = 0

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

Divide each side by '9'.
0.5555555556 + 3.555555556v + v2 = 0

Move the constant term to the right:

Add '-0.5555555556' to each side of the equation.
0.5555555556 + 3.555555556v + -0.5555555556 + v2 = 0 + -0.5555555556

Reorder the terms:
0.5555555556 + -0.5555555556 + 3.555555556v + v2 = 0 + -0.5555555556

Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000
0.0000000000 + 3.555555556v + v2 = 0 + -0.5555555556
3.555555556v + v2 = 0 + -0.5555555556

Combine like terms: 0 + -0.5555555556 = -0.5555555556
3.555555556v + v2 = -0.5555555556

The v term is 3.555555556v.  Take half its coefficient (1.777777778).
Square it (3.160493828) and add it to both sides.

Add '3.160493828' to each side of the equation.
3.555555556v + 3.160493828 + v2 = -0.5555555556 + 3.160493828

Reorder the terms:
3.160493828 + 3.555555556v + v2 = -0.5555555556 + 3.160493828

Combine like terms: -0.5555555556 + 3.160493828 = 2.6049382724
3.160493828 + 3.555555556v + v2 = 2.6049382724

Factor a perfect square on the left side:
(v + 1.777777778)(v + 1.777777778) = 2.6049382724

Calculate the square root of the right side: 1.613982117

Break this problem into two subproblems by setting 
(v + 1.777777778) equal to 1.613982117 and -1.613982117.

Subproblem 1
v + 1.777777778 = 1.613982117

Simplifying
v + 1.777777778 = 1.613982117

Reorder the terms:
1.777777778 + v = 1.613982117

Solving
1.777777778 + v = 1.613982117

Solving for variable 'v'.

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

Add '-1.777777778' to each side of the equation.
1.777777778 + -1.777777778 + v = 1.613982117 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + v = 1.613982117 + -1.777777778
v = 1.613982117 + -1.777777778

Combine like terms: 1.613982117 + -1.777777778 = -0.163795661
v = -0.163795661

Simplifying
v = -0.163795661

Subproblem 2
v + 1.777777778 = -1.613982117

Simplifying
v + 1.777777778 = -1.613982117

Reorder the terms:
1.777777778 + v = -1.613982117

Solving
1.777777778 + v = -1.613982117

Solving for variable 'v'.

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

Add '-1.777777778' to each side of the equation.
1.777777778 + -1.777777778 + v = -1.613982117 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + v = -1.613982117 + -1.777777778
v = -1.613982117 + -1.777777778

Combine like terms: -1.613982117 + -1.777777778 = -3.391759895
v = -3.391759895

Simplifying
v = -3.391759895

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.163795661, -3.391759895}
Solution
v = {-0.163795661, -3.391759895}