-6v-4=-4v(v-3)

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Solution for -6v-4=-4v(v-3) equation: 


Simplifying
-6v + -4 = -4v(v + -3)

Reorder the terms:
-4 + -6v = -4v(v + -3)

Reorder the terms:
-4 + -6v = -4v(-3 + v)
-4 + -6v = (-3 * -4v + v * -4v)
-4 + -6v = (12v + -4v2)

Solving
-4 + -6v = 12v + -4v2

Solving for variable 'v'.

Combine like terms: -6v + -12v = -18v
-4 + -18v + 4v2 = 12v + -4v2 + -12v + 4v2

Reorder the terms:
-4 + -18v + 4v2 = 12v + -12v + -4v2 + 4v2

Combine like terms: 12v + -12v = 0
-4 + -18v + 4v2 = 0 + -4v2 + 4v2
-4 + -18v + 4v2 = -4v2 + 4v2

Combine like terms: -4v2 + 4v2 = 0
-4 + -18v + 4v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -9v + 2v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -9v + 2v2)' equal to zero and attempt to solve:

Simplifying
-2 + -9v + 2v2 = 0

Solving
-2 + -9v + 2v2 = 0

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

Divide each side by '2'.
-1 + -4.5v + v2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.5v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.5v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.5v + v2 = 0 + 1
-4.5v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.5v + v2 = 1

The v term is -4.5v.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5v + 5.0625 + v2 = 1 + 5.0625

Reorder the terms:
5.0625 + -4.5v + v2 = 1 + 5.0625

Combine like terms: 1 + 5.0625 = 6.0625
5.0625 + -4.5v + v2 = 6.0625

Factor a perfect square on the left side:
(v + -2.25)(v + -2.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(v + -2.25) equal to 2.46221445 and -2.46221445.


Subproblem 1
v + -2.25 = 2.46221445

Simplifying
v + -2.25 = 2.46221445

Reorder the terms:
-2.25 + v = 2.46221445

Solving
-2.25 + v = 2.46221445

Solving for variable 'v'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + v = 2.46221445 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + v = 2.46221445 + 2.25
v = 2.46221445 + 2.25

Combine like terms: 2.46221445 + 2.25 = 4.71221445
v = 4.71221445

Simplifying
v = 4.71221445


Subproblem 2
v + -2.25 = -2.46221445

Simplifying
v + -2.25 = -2.46221445

Reorder the terms:
-2.25 + v = -2.46221445

Solving
-2.25 + v = -2.46221445

Solving for variable 'v'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + v = -2.46221445 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + v = -2.46221445 + 2.25
v = -2.46221445 + 2.25

Combine like terms: -2.46221445 + 2.25 = -0.21221445
v = -0.21221445

Simplifying
v = -0.21221445


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.71221445, -0.21221445}
Solution
v = {4.71221445, -0.21221445}

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