3v=(5+7v)(v-3)

Solution for 3v=(5+7v)(v-3) equation:

Simplifying
3v = (5 + 7v)(v + -3)

Reorder the terms:
3v = (5 + 7v)(-3 + v)

Multiply (5 + 7v) * (-3 + v)
3v = (5(-3 + v) + 7v * (-3 + v))
3v = ((-3 * 5 + v * 5) + 7v * (-3 + v))
3v = ((-15 + 5v) + 7v * (-3 + v))
3v = (-15 + 5v + (-3 * 7v + v * 7v))
3v = (-15 + 5v + (-21v + 7v2))

Combine like terms: 5v + -21v = -16v
3v = (-15 + -16v + 7v2)

Solving
3v = -15 + -16v + 7v2

Solving for variable 'v'.

Reorder the terms:
15 + 3v + 16v + -7v2 = -15 + -16v + 7v2 + 15 + 16v + -7v2

Combine like terms: 3v + 16v = 19v
15 + 19v + -7v2 = -15 + -16v + 7v2 + 15 + 16v + -7v2

Reorder the terms:
15 + 19v + -7v2 = -15 + 15 + -16v + 16v + 7v2 + -7v2

Combine like terms: -15 + 15 = 0
15 + 19v + -7v2 = 0 + -16v + 16v + 7v2 + -7v2
15 + 19v + -7v2 = -16v + 16v + 7v2 + -7v2

Combine like terms: -16v + 16v = 0
15 + 19v + -7v2 = 0 + 7v2 + -7v2
15 + 19v + -7v2 = 7v2 + -7v2

Combine like terms: 7v2 + -7v2 = 0
15 + 19v + -7v2 = 0

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

Divide each side by '-7'.
-2.142857143 + -2.714285714v + v2 = 0

Move the constant term to the right:

Add '2.142857143' to each side of the equation.
-2.142857143 + -2.714285714v + 2.142857143 + v2 = 0 + 2.142857143

Reorder the terms:
-2.142857143 + 2.142857143 + -2.714285714v + v2 = 0 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + -2.714285714v + v2 = 0 + 2.142857143
-2.714285714v + v2 = 0 + 2.142857143

Combine like terms: 0 + 2.142857143 = 2.142857143
-2.714285714v + v2 = 2.142857143

The v term is -2.714285714v.  Take half its coefficient (-1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
-2.714285714v + 1.841836734 + v2 = 2.142857143 + 1.841836734

Reorder the terms:
1.841836734 + -2.714285714v + v2 = 2.142857143 + 1.841836734

Combine like terms: 2.142857143 + 1.841836734 = 3.984693877
1.841836734 + -2.714285714v + v2 = 3.984693877

Factor a perfect square on the left side:
(v + -1.357142857)(v + -1.357142857) = 3.984693877

Calculate the square root of the right side: 1.996169802

Break this problem into two subproblems by setting 
(v + -1.357142857) equal to 1.996169802 and -1.996169802.

Subproblem 1
v + -1.357142857 = 1.996169802

Simplifying
v + -1.357142857 = 1.996169802

Reorder the terms:
-1.357142857 + v = 1.996169802

Solving
-1.357142857 + v = 1.996169802

Solving for variable 'v'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + v = 1.996169802 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + v = 1.996169802 + 1.357142857
v = 1.996169802 + 1.357142857

Combine like terms: 1.996169802 + 1.357142857 = 3.353312659
v = 3.353312659

Simplifying
v = 3.353312659

Subproblem 2
v + -1.357142857 = -1.996169802

Simplifying
v + -1.357142857 = -1.996169802

Reorder the terms:
-1.357142857 + v = -1.996169802

Solving
-1.357142857 + v = -1.996169802

Solving for variable 'v'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + v = -1.996169802 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + v = -1.996169802 + 1.357142857
v = -1.996169802 + 1.357142857

Combine like terms: -1.996169802 + 1.357142857 = -0.639026945
v = -0.639026945

Simplifying
v = -0.639026945

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.353312659, -0.639026945}