3v(v-5)=8

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Solution for 3v(v-5)=8 equation: 


Simplifying
3v(v + -5) = 8

Reorder the terms:
3v(-5 + v) = 8
(-5 * 3v + v * 3v) = 8
(-15v + 3v2) = 8

Solving
-15v + 3v2 = 8

Solving for variable 'v'.

Reorder the terms:
-8 + -15v + 3v2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -15v + 3v2 = 0

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

Divide each side by '3'.
-2.666666667 + -5v + v2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -5v + 2.666666667 + v2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -5v + v2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -5v + v2 = 0 + 2.666666667
-5v + v2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-5v + v2 = 2.666666667

The v term is -5v.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5v + 6.25 + v2 = 2.666666667 + 6.25

Reorder the terms:
6.25 + -5v + v2 = 2.666666667 + 6.25

Combine like terms: 2.666666667 + 6.25 = 8.916666667
6.25 + -5v + v2 = 8.916666667

Factor a perfect square on the left side:
(v + -2.5)(v + -2.5) = 8.916666667

Calculate the square root of the right side: 2.986078811

Break this problem into two subproblems by setting 
(v + -2.5) equal to 2.986078811 and -2.986078811.


Subproblem 1
v + -2.5 = 2.986078811

Simplifying
v + -2.5 = 2.986078811

Reorder the terms:
-2.5 + v = 2.986078811

Solving
-2.5 + v = 2.986078811

Solving for variable 'v'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + v = 2.986078811 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + v = 2.986078811 + 2.5
v = 2.986078811 + 2.5

Combine like terms: 2.986078811 + 2.5 = 5.486078811
v = 5.486078811

Simplifying
v = 5.486078811


Subproblem 2
v + -2.5 = -2.986078811

Simplifying
v + -2.5 = -2.986078811

Reorder the terms:
-2.5 + v = -2.986078811

Solving
-2.5 + v = -2.986078811

Solving for variable 'v'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + v = -2.986078811 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + v = -2.986078811 + 2.5
v = -2.986078811 + 2.5

Combine like terms: -2.986078811 + 2.5 = -0.486078811
v = -0.486078811

Simplifying
v = -0.486078811


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {5.486078811, -0.486078811}

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