-3v^2-20v+12=0

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Solution for -3v^2-20v+12=0 equation: 


Simplifying
-3v2 + -20v + 12 = 0

Reorder the terms:
12 + -20v + -3v2 = 0

Solving
12 + -20v + -3v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4 + 6.666666667v + v2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6.666666667v + 4 + v2 = 0 + 4

Reorder the terms:
-4 + 4 + 6.666666667v + v2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6.666666667v + v2 = 0 + 4
6.666666667v + v2 = 0 + 4

Combine like terms: 0 + 4 = 4
6.666666667v + v2 = 4

The v term is 6.666666667v.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667v + 11.11111112 + v2 = 4 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667v + v2 = 4 + 11.11111112

Combine like terms: 4 + 11.11111112 = 15.11111112
11.11111112 + 6.666666667v + v2 = 15.11111112

Factor a perfect square on the left side:
(v + 3.333333334)(v + 3.333333334) = 15.11111112

Calculate the square root of the right side: 3.887301264

Break this problem into two subproblems by setting 
(v + 3.333333334) equal to 3.887301264 and -3.887301264.


Subproblem 1
v + 3.333333334 = 3.887301264

Simplifying
v + 3.333333334 = 3.887301264

Reorder the terms:
3.333333334 + v = 3.887301264

Solving
3.333333334 + v = 3.887301264

Solving for variable 'v'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + v = 3.887301264 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + v = 3.887301264 + -3.333333334
v = 3.887301264 + -3.333333334

Combine like terms: 3.887301264 + -3.333333334 = 0.55396793
v = 0.55396793

Simplifying
v = 0.55396793


Subproblem 2
v + 3.333333334 = -3.887301264

Simplifying
v + 3.333333334 = -3.887301264

Reorder the terms:
3.333333334 + v = -3.887301264

Solving
3.333333334 + v = -3.887301264

Solving for variable 'v'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + v = -3.887301264 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + v = -3.887301264 + -3.333333334
v = -3.887301264 + -3.333333334

Combine like terms: -3.887301264 + -3.333333334 = -7.220634598
v = -7.220634598

Simplifying
v = -7.220634598


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.55396793, -7.220634598}

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