2=(v-7)(v-1)

Solution for 2=(v-7)(v-1) equation:

Simplifying
2 = (v + -7)(v + -1)

Reorder the terms:
2 = (-7 + v)(v + -1)

Reorder the terms:
2 = (-7 + v)(-1 + v)

Multiply (-7 + v) * (-1 + v)
2 = (-7(-1 + v) + v(-1 + v))
2 = ((-1 * -7 + v * -7) + v(-1 + v))
2 = ((7 + -7v) + v(-1 + v))
2 = (7 + -7v + (-1 * v + v * v))
2 = (7 + -7v + (-1v + v2))

Combine like terms: -7v + -1v = -8v
2 = (7 + -8v + v2)

Solving
2 = 7 + -8v + v2

Solving for variable 'v'.

Combine like terms: 2 + -7 = -5
-5 + 8v + -1v2 = 7 + -8v + v2 + -7 + 8v + -1v2

Reorder the terms:
-5 + 8v + -1v2 = 7 + -7 + -8v + 8v + v2 + -1v2

Combine like terms: 7 + -7 = 0
-5 + 8v + -1v2 = 0 + -8v + 8v + v2 + -1v2
-5 + 8v + -1v2 = -8v + 8v + v2 + -1v2

Combine like terms: -8v + 8v = 0
-5 + 8v + -1v2 = 0 + v2 + -1v2
-5 + 8v + -1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-5 + 8v + -1v2 = 0

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

Divide each side by '-1'.
5 + -8v + v2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8v + -5 + v2 = 0 + -5

Reorder the terms:
5 + -5 + -8v + v2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8v + v2 = 0 + -5
-8v + v2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8v + v2 = -5

The v term is -8v.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8v + 16 + v2 = -5 + 16

Reorder the terms:
16 + -8v + v2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8v + v2 = 11

Factor a perfect square on the left side:
(v + -4)(v + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(v + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1
v + -4 = 3.31662479

Simplifying
v + -4 = 3.31662479

Reorder the terms:
-4 + v = 3.31662479

Solving
-4 + v = 3.31662479

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = 3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + v = 3.31662479 + 4
v = 3.31662479 + 4

Combine like terms: 3.31662479 + 4 = 7.31662479
v = 7.31662479

Simplifying
v = 7.31662479

Subproblem 2
v + -4 = -3.31662479

Simplifying
v + -4 = -3.31662479

Reorder the terms:
-4 + v = -3.31662479

Solving
-4 + v = -3.31662479

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = -3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + v = -3.31662479 + 4
v = -3.31662479 + 4

Combine like terms: -3.31662479 + 4 = 0.68337521
v = 0.68337521

Simplifying
v = 0.68337521

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {7.31662479, 0.68337521}