2(5-3v)9v=28

Solution for 2(5-3v)9v=28 equation:

Simplifying
2(5 + -3v) * 9v = 28

Reorder the terms for easier multiplication:
2 * 9v(5 + -3v) = 28

Multiply 2 * 9
18v(5 + -3v) = 28
(5 * 18v + -3v * 18v) = 28
(90v + -54v2) = 28

Solving
90v + -54v2 = 28

Solving for variable 'v'.

Reorder the terms:
-28 + 90v + -54v2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 90v + -54v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 45v + -27v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + 45v + -27v2)' equal to zero and attempt to solve:

Simplifying
-14 + 45v + -27v2 = 0

Solving
-14 + 45v + -27v2 = 0

Begin completing the square.  Divide all terms by
-27 the coefficient of the squared term: 

Divide each side by '-27'.
0.5185185185 + -1.666666667v + v2 = 0

Move the constant term to the right:

Add '-0.5185185185' to each side of the equation.
0.5185185185 + -1.666666667v + -0.5185185185 + v2 = 0 + -0.5185185185

Reorder the terms:
0.5185185185 + -0.5185185185 + -1.666666667v + v2 = 0 + -0.5185185185

Combine like terms: 0.5185185185 + -0.5185185185 = 0.0000000000
0.0000000000 + -1.666666667v + v2 = 0 + -0.5185185185
-1.666666667v + v2 = 0 + -0.5185185185

Combine like terms: 0 + -0.5185185185 = -0.5185185185
-1.666666667v + v2 = -0.5185185185

The v term is -1.666666667v.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667v + 0.6944444447 + v2 = -0.5185185185 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667v + v2 = -0.5185185185 + 0.6944444447

Combine like terms: -0.5185185185 + 0.6944444447 = 0.1759259262
0.6944444447 + -1.666666667v + v2 = 0.1759259262

Factor a perfect square on the left side:
(v + -0.8333333335)(v + -0.8333333335) = 0.1759259262

Calculate the square root of the right side: 0.419435247

Break this problem into two subproblems by setting 
(v + -0.8333333335) equal to 0.419435247 and -0.419435247.

Subproblem 1
v + -0.8333333335 = 0.419435247

Simplifying
v + -0.8333333335 = 0.419435247

Reorder the terms:
-0.8333333335 + v = 0.419435247

Solving
-0.8333333335 + v = 0.419435247

Solving for variable 'v'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + v = 0.419435247 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + v = 0.419435247 + 0.8333333335
v = 0.419435247 + 0.8333333335

Combine like terms: 0.419435247 + 0.8333333335 = 1.2527685805
v = 1.2527685805

Simplifying
v = 1.2527685805

Subproblem 2
v + -0.8333333335 = -0.419435247

Simplifying
v + -0.8333333335 = -0.419435247

Reorder the terms:
-0.8333333335 + v = -0.419435247

Solving
-0.8333333335 + v = -0.419435247

Solving for variable 'v'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + v = -0.419435247 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + v = -0.419435247 + 0.8333333335
v = -0.419435247 + 0.8333333335

Combine like terms: -0.419435247 + 0.8333333335 = 0.4138980865
v = 0.4138980865

Simplifying
v = 0.4138980865

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.2527685805, 0.4138980865}
Solution
v = {1.2527685805, 0.4138980865}