-2v^2-v+12=-3v+6v

Solution for -2v^2-v+12=-3v+6v equation:

Simplifying
-2v2 + -1v + 12 = -3v + 6v

Reorder the terms:
12 + -1v + -2v2 = -3v + 6v

Combine like terms: -3v + 6v = 3v
12 + -1v + -2v2 = 3v

Solving
12 + -1v + -2v2 = 3v

Solving for variable 'v'.

Reorder the terms:
12 + -1v + -3v + -2v2 = 3v + -3v

Combine like terms: -1v + -3v = -4v
12 + -4v + -2v2 = 3v + -3v

Combine like terms: 3v + -3v = 0
12 + -4v + -2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -2v + -1v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -2v + -1v2)' equal to zero and attempt to solve:

Simplifying
6 + -2v + -1v2 = 0

Solving
6 + -2v + -1v2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 2v + v2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2v + 6 + v2 = 0 + 6

Reorder the terms:
-6 + 6 + 2v + v2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2v + v2 = 0 + 6
2v + v2 = 0 + 6

Combine like terms: 0 + 6 = 6
2v + v2 = 6

The v term is 2v.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2v + 1 + v2 = 6 + 1

Reorder the terms:
1 + 2v + v2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2v + v2 = 7

Factor a perfect square on the left side:
(v + 1)(v + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(v + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
v + 1 = 2.645751311

Simplifying
v + 1 = 2.645751311

Reorder the terms:
1 + v = 2.645751311

Solving
1 + v = 2.645751311

Solving for variable 'v'.

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

Add '-1' to each side of the equation.
1 + -1 + v = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + v = 2.645751311 + -1
v = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
v = 1.645751311

Simplifying
v = 1.645751311

Subproblem 2
v + 1 = -2.645751311

Simplifying
v + 1 = -2.645751311

Reorder the terms:
1 + v = -2.645751311

Solving
1 + v = -2.645751311

Solving for variable 'v'.

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

Add '-1' to each side of the equation.
1 + -1 + v = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + v = -2.645751311 + -1
v = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
v = -3.645751311

Simplifying
v = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.645751311, -3.645751311}
Solution
v = {1.645751311, -3.645751311}