4-2v(v-6)=8

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Solution for 4-2v(v-6)=8 equation: 


Simplifying
4 + -2v(v + -6) = 8

Reorder the terms:
4 + -2v(-6 + v) = 8
4 + (-6 * -2v + v * -2v) = 8
4 + (12v + -2v2) = 8

Solving
4 + 12v + -2v2 = 8

Solving for variable 'v'.

Reorder the terms:
4 + -8 + 12v + -2v2 = 8 + -8

Combine like terms: 4 + -8 = -4
-4 + 12v + -2v2 = 8 + -8

Combine like terms: 8 + -8 = 0
-4 + 12v + -2v2 = 0

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

Ignore the factor 2.

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

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

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

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

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

Move the constant term to the right:

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

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

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

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

The v term is -6v.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6v + 9 + v2 = -2 + 9

Reorder the terms:
9 + -6v + v2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6v + v2 = 7

Factor a perfect square on the left side:
(v + -3)(v + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(v + -3) equal to 2.645751311 and -2.645751311.


Subproblem 1
v + -3 = 2.645751311

Simplifying
v + -3 = 2.645751311

Reorder the terms:
-3 + v = 2.645751311

Solving
-3 + v = 2.645751311

Solving for variable 'v'.

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

Add '3' to each side of the equation.
-3 + 3 + v = 2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + v = 2.645751311 + 3
v = 2.645751311 + 3

Combine like terms: 2.645751311 + 3 = 5.645751311
v = 5.645751311

Simplifying
v = 5.645751311


Subproblem 2
v + -3 = -2.645751311

Simplifying
v + -3 = -2.645751311

Reorder the terms:
-3 + v = -2.645751311

Solving
-3 + v = -2.645751311

Solving for variable 'v'.

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

Add '3' to each side of the equation.
-3 + 3 + v = -2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + v = -2.645751311 + 3
v = -2.645751311 + 3

Combine like terms: -2.645751311 + 3 = 0.354248689
v = 0.354248689

Simplifying
v = 0.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {5.645751311, 0.354248689}
Solution
v = {5.645751311, 0.354248689}

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