-3(v+5)5v=2(v-6)

Solution for -3(v+5)5v=2(v-6) equation:

Simplifying
-3(v + 5) * 5v = 2(v + -6)

Reorder the terms:
-3(5 + v) * 5v = 2(v + -6)

Reorder the terms for easier multiplication:
-3 * 5v(5 + v) = 2(v + -6)

Multiply -3 * 5
-15v(5 + v) = 2(v + -6)
(5 * -15v + v * -15v) = 2(v + -6)
(-75v + -15v2) = 2(v + -6)

Reorder the terms:
-75v + -15v2 = 2(-6 + v)
-75v + -15v2 = (-6 * 2 + v * 2)
-75v + -15v2 = (-12 + 2v)

Solving
-75v + -15v2 = -12 + 2v

Solving for variable 'v'.

Reorder the terms:
12 + -75v + -2v + -15v2 = -12 + 2v + 12 + -2v

Combine like terms: -75v + -2v = -77v
12 + -77v + -15v2 = -12 + 2v + 12 + -2v

Reorder the terms:
12 + -77v + -15v2 = -12 + 12 + 2v + -2v

Combine like terms: -12 + 12 = 0
12 + -77v + -15v2 = 0 + 2v + -2v
12 + -77v + -15v2 = 2v + -2v

Combine like terms: 2v + -2v = 0
12 + -77v + -15v2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-0.8 + 5.133333333v + v2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 5.133333333v + 0.8 + v2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 5.133333333v + v2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 5.133333333v + v2 = 0 + 0.8
5.133333333v + v2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
5.133333333v + v2 = 0.8

The v term is 5.133333333v.  Take half its coefficient (2.566666667).
Square it (6.587777779) and add it to both sides.

Add '6.587777779' to each side of the equation.
5.133333333v + 6.587777779 + v2 = 0.8 + 6.587777779

Reorder the terms:
6.587777779 + 5.133333333v + v2 = 0.8 + 6.587777779

Combine like terms: 0.8 + 6.587777779 = 7.387777779
6.587777779 + 5.133333333v + v2 = 7.387777779

Factor a perfect square on the left side:
(v + 2.566666667)(v + 2.566666667) = 7.387777779

Calculate the square root of the right side: 2.718046684

Break this problem into two subproblems by setting 
(v + 2.566666667) equal to 2.718046684 and -2.718046684.

Subproblem 1
v + 2.566666667 = 2.718046684

Simplifying
v + 2.566666667 = 2.718046684

Reorder the terms:
2.566666667 + v = 2.718046684

Solving
2.566666667 + v = 2.718046684

Solving for variable 'v'.

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

Add '-2.566666667' to each side of the equation.
2.566666667 + -2.566666667 + v = 2.718046684 + -2.566666667

Combine like terms: 2.566666667 + -2.566666667 = 0.000000000
0.000000000 + v = 2.718046684 + -2.566666667
v = 2.718046684 + -2.566666667

Combine like terms: 2.718046684 + -2.566666667 = 0.151380017
v = 0.151380017

Simplifying
v = 0.151380017

Subproblem 2
v + 2.566666667 = -2.718046684

Simplifying
v + 2.566666667 = -2.718046684

Reorder the terms:
2.566666667 + v = -2.718046684

Solving
2.566666667 + v = -2.718046684

Solving for variable 'v'.

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

Add '-2.566666667' to each side of the equation.
2.566666667 + -2.566666667 + v = -2.718046684 + -2.566666667

Combine like terms: 2.566666667 + -2.566666667 = 0.000000000
0.000000000 + v = -2.718046684 + -2.566666667
v = -2.718046684 + -2.566666667

Combine like terms: -2.718046684 + -2.566666667 = -5.284713351
v = -5.284713351

Simplifying
v = -5.284713351

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.151380017, -5.284713351}