7v(6-2v)=12

Solution for 7v(6-2v)=12 equation:

Simplifying
7v(6 + -2v) = 12
(6 * 7v + -2v * 7v) = 12
(42v + -14v2) = 12

Solving
42v + -14v2 = 12

Solving for variable 'v'.

Reorder the terms:
-12 + 42v + -14v2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 42v + -14v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 21v + -7v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 21v + -7v2)' equal to zero and attempt to solve:

Simplifying
-6 + 21v + -7v2 = 0

Solving
-6 + 21v + -7v2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.8571428571 + -3v + v2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + -3v + -0.8571428571 + v2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + -3v + v2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + -3v + v2 = 0 + -0.8571428571
-3v + v2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
-3v + v2 = -0.8571428571

The v term is -3v.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3v + 2.25 + v2 = -0.8571428571 + 2.25

Reorder the terms:
2.25 + -3v + v2 = -0.8571428571 + 2.25

Combine like terms: -0.8571428571 + 2.25 = 1.3928571429
2.25 + -3v + v2 = 1.3928571429

Factor a perfect square on the left side:
(v + -1.5)(v + -1.5) = 1.3928571429

Calculate the square root of the right side: 1.180193689

Break this problem into two subproblems by setting 
(v + -1.5) equal to 1.180193689 and -1.180193689.

Subproblem 1
v + -1.5 = 1.180193689

Simplifying
v + -1.5 = 1.180193689

Reorder the terms:
-1.5 + v = 1.180193689

Solving
-1.5 + v = 1.180193689

Solving for variable 'v'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + v = 1.180193689 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + v = 1.180193689 + 1.5
v = 1.180193689 + 1.5

Combine like terms: 1.180193689 + 1.5 = 2.680193689
v = 2.680193689

Simplifying
v = 2.680193689

Subproblem 2
v + -1.5 = -1.180193689

Simplifying
v + -1.5 = -1.180193689

Reorder the terms:
-1.5 + v = -1.180193689

Solving
-1.5 + v = -1.180193689

Solving for variable 'v'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + v = -1.180193689 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + v = -1.180193689 + 1.5
v = -1.180193689 + 1.5

Combine like terms: -1.180193689 + 1.5 = 0.319806311
v = 0.319806311

Simplifying
v = 0.319806311

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.680193689, 0.319806311}
Solution
v = {2.680193689, 0.319806311}