3(10-6v)3v=15

Solution for 3(10-6v)3v=15 equation:

Simplifying
3(10 + -6v) * 3v = 15

Reorder the terms for easier multiplication:
3 * 3v(10 + -6v) = 15

Multiply 3 * 3
9v(10 + -6v) = 15
(10 * 9v + -6v * 9v) = 15
(90v + -54v2) = 15

Solving
90v + -54v2 = 15

Solving for variable 'v'.

Reorder the terms:
-15 + 90v + -54v2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 90v + -54v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 30v + -18v2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + 30v + -18v2)' equal to zero and attempt to solve:

Simplifying
-5 + 30v + -18v2 = 0

Solving
-5 + 30v + -18v2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
0.2777777778 + -1.666666667v + v2 = 0

Move the constant term to the right:

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -1.666666667v + -0.2777777778 + v2 = 0 + -0.2777777778

Reorder the terms:
0.2777777778 + -0.2777777778 + -1.666666667v + v2 = 0 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + -1.666666667v + v2 = 0 + -0.2777777778
-1.666666667v + v2 = 0 + -0.2777777778

Combine like terms: 0 + -0.2777777778 = -0.2777777778
-1.666666667v + v2 = -0.2777777778

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 = -0.2777777778 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667v + v2 = -0.2777777778 + 0.6944444447

Combine like terms: -0.2777777778 + 0.6944444447 = 0.4166666669
0.6944444447 + -1.666666667v + v2 = 0.4166666669

Factor a perfect square on the left side:
(v + -0.8333333335)(v + -0.8333333335) = 0.4166666669

Calculate the square root of the right side: 0.645497225

Break this problem into two subproblems by setting 
(v + -0.8333333335) equal to 0.645497225 and -0.645497225.

Subproblem 1
v + -0.8333333335 = 0.645497225

Simplifying
v + -0.8333333335 = 0.645497225

Reorder the terms:
-0.8333333335 + v = 0.645497225

Solving
-0.8333333335 + v = 0.645497225

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 = 0.645497225 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + v = 0.645497225 + 0.8333333335
v = 0.645497225 + 0.8333333335

Combine like terms: 0.645497225 + 0.8333333335 = 1.4788305585
v = 1.4788305585

Simplifying
v = 1.4788305585

Subproblem 2
v + -0.8333333335 = -0.645497225

Simplifying
v + -0.8333333335 = -0.645497225

Reorder the terms:
-0.8333333335 + v = -0.645497225

Solving
-0.8333333335 + v = -0.645497225

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 = -0.645497225 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + v = -0.645497225 + 0.8333333335
v = -0.645497225 + 0.8333333335

Combine like terms: -0.645497225 + 0.8333333335 = 0.1878361085
v = 0.1878361085

Simplifying
v = 0.1878361085

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.4788305585, 0.1878361085}
Solution
v = {1.4788305585, 0.1878361085}