6v^2-15v+3=0

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


Simplifying
6v2 + -15v + 3 = 0

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

Solving
3 + -15v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -5v + 2v2) = 0

Ignore the factor 3.

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 = 2.280776406
v = 2.280776406

Simplifying
v = 2.280776406


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 = 0.219223594
v = 0.219223594

Simplifying
v = 0.219223594


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

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