6v^2-3v-15-2v=0

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Solution for 6v^2-3v-15-2v=0 equation: 


Simplifying
6v2 + -3v + -15 + -2v = 0

Reorder the terms:
-15 + -3v + -2v + 6v2 = 0

Combine like terms: -3v + -2v = -5v
-15 + -5v + 6v2 = 0

Solving
-15 + -5v + 6v2 = 0

Solving for variable 'v'.

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

Divide each side by '6'.
-2.5 + -0.8333333333v + v2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.8333333333v + 2.5 + v2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.8333333333v + v2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.8333333333v + v2 = 0 + 2.5
-0.8333333333v + v2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.8333333333v + v2 = 2.5

The v term is -0.8333333333v.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333v + 0.1736111111 + v2 = 2.5 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333v + v2 = 2.5 + 0.1736111111

Combine like terms: 2.5 + 0.1736111111 = 2.6736111111
0.1736111111 + -0.8333333333v + v2 = 2.6736111111

Factor a perfect square on the left side:
(v + -0.4166666667)(v + -0.4166666667) = 2.6736111111

Calculate the square root of the right side: 1.635118073

Break this problem into two subproblems by setting 
(v + -0.4166666667) equal to 1.635118073 and -1.635118073.


Subproblem 1
v + -0.4166666667 = 1.635118073

Simplifying
v + -0.4166666667 = 1.635118073

Reorder the terms:
-0.4166666667 + v = 1.635118073

Solving
-0.4166666667 + v = 1.635118073

Solving for variable 'v'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + v = 1.635118073 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + v = 1.635118073 + 0.4166666667
v = 1.635118073 + 0.4166666667

Combine like terms: 1.635118073 + 0.4166666667 = 2.0517847397
v = 2.0517847397

Simplifying
v = 2.0517847397


Subproblem 2
v + -0.4166666667 = -1.635118073

Simplifying
v + -0.4166666667 = -1.635118073

Reorder the terms:
-0.4166666667 + v = -1.635118073

Solving
-0.4166666667 + v = -1.635118073

Solving for variable 'v'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + v = -1.635118073 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + v = -1.635118073 + 0.4166666667
v = -1.635118073 + 0.4166666667

Combine like terms: -1.635118073 + 0.4166666667 = -1.2184514063
v = -1.2184514063

Simplifying
v = -1.2184514063


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.0517847397, -1.2184514063}

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