3(2v-2)3v+5=4(v+5)+2v

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Solution for 3(2v-2)3v+5=4(v+5)+2v equation: 


Simplifying
3(2v + -2) * 3v + 5 = 4(v + 5) + 2v

Reorder the terms:
3(-2 + 2v) * 3v + 5 = 4(v + 5) + 2v

Reorder the terms for easier multiplication:
3 * 3v(-2 + 2v) + 5 = 4(v + 5) + 2v

Multiply 3 * 3
9v(-2 + 2v) + 5 = 4(v + 5) + 2v
(-2 * 9v + 2v * 9v) + 5 = 4(v + 5) + 2v
(-18v + 18v2) + 5 = 4(v + 5) + 2v

Reorder the terms:
5 + -18v + 18v2 = 4(v + 5) + 2v

Reorder the terms:
5 + -18v + 18v2 = 4(5 + v) + 2v
5 + -18v + 18v2 = (5 * 4 + v * 4) + 2v
5 + -18v + 18v2 = (20 + 4v) + 2v

Combine like terms: 4v + 2v = 6v
5 + -18v + 18v2 = 20 + 6v

Solving
5 + -18v + 18v2 = 20 + 6v

Solving for variable 'v'.

Reorder the terms:
5 + -20 + -18v + -6v + 18v2 = 20 + 6v + -20 + -6v

Combine like terms: 5 + -20 = -15
-15 + -18v + -6v + 18v2 = 20 + 6v + -20 + -6v

Combine like terms: -18v + -6v = -24v
-15 + -24v + 18v2 = 20 + 6v + -20 + -6v

Reorder the terms:
-15 + -24v + 18v2 = 20 + -20 + 6v + -6v

Combine like terms: 20 + -20 = 0
-15 + -24v + 18v2 = 0 + 6v + -6v
-15 + -24v + 18v2 = 6v + -6v

Combine like terms: 6v + -6v = 0
-15 + -24v + 18v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -8v + 6v2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -8v + 6v2)' equal to zero and attempt to solve:

Simplifying
-5 + -8v + 6v2 = 0

Solving
-5 + -8v + 6v2 = 0

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

Divide each side by '6'.
-0.8333333333 + -1.333333333v + v2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -1.333333333v + 0.8333333333 + v2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -1.333333333v + v2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -1.333333333v + v2 = 0 + 0.8333333333
-1.333333333v + v2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-1.333333333v + v2 = 0.8333333333

The v term is -1.333333333v.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333v + 0.4444444442 + v2 = 0.8333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333v + v2 = 0.8333333333 + 0.4444444442

Combine like terms: 0.8333333333 + 0.4444444442 = 1.2777777775
0.4444444442 + -1.333333333v + v2 = 1.2777777775

Factor a perfect square on the left side:
(v + -0.6666666665)(v + -0.6666666665) = 1.2777777775

Calculate the square root of the right side: 1.13038833

Break this problem into two subproblems by setting 
(v + -0.6666666665) equal to 1.13038833 and -1.13038833.


Subproblem 1
v + -0.6666666665 = 1.13038833

Simplifying
v + -0.6666666665 = 1.13038833

Reorder the terms:
-0.6666666665 + v = 1.13038833

Solving
-0.6666666665 + v = 1.13038833

Solving for variable 'v'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + v = 1.13038833 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + v = 1.13038833 + 0.6666666665
v = 1.13038833 + 0.6666666665

Combine like terms: 1.13038833 + 0.6666666665 = 1.7970549965
v = 1.7970549965

Simplifying
v = 1.7970549965


Subproblem 2
v + -0.6666666665 = -1.13038833

Simplifying
v + -0.6666666665 = -1.13038833

Reorder the terms:
-0.6666666665 + v = -1.13038833

Solving
-0.6666666665 + v = -1.13038833

Solving for variable 'v'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + v = -1.13038833 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + v = -1.13038833 + 0.6666666665
v = -1.13038833 + 0.6666666665

Combine like terms: -1.13038833 + 0.6666666665 = -0.4637216635
v = -0.4637216635

Simplifying
v = -0.4637216635


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.7970549965, -0.4637216635}
Solution
v = {1.7970549965, -0.4637216635}

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