3(v+6)6v=30

Solution for 3(v+6)6v=30 equation:

Simplifying
3(v + 6) * 6v = 30

Reorder the terms:
3(6 + v) * 6v = 30

Reorder the terms for easier multiplication:
3 * 6v(6 + v) = 30

Multiply 3 * 6
18v(6 + v) = 30
(6 * 18v + v * 18v) = 30
(108v + 18v2) = 30

Solving
108v + 18v2 = 30

Solving for variable 'v'.

Reorder the terms:
-30 + 108v + 18v2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 108v + 18v2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + 18v + 3v2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + 18v + 3v2)' equal to zero and attempt to solve:

Simplifying
-5 + 18v + 3v2 = 0

Solving
-5 + 18v + 3v2 = 0

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

Divide each side by '3'.
-1.666666667 + 6v + v2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 6v + 1.666666667 + v2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 6v + v2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 6v + v2 = 0 + 1.666666667
6v + v2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
6v + v2 = 1.666666667

The v term is 6v.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6v + 9 + v2 = 1.666666667 + 9

Reorder the terms:
9 + 6v + v2 = 1.666666667 + 9

Combine like terms: 1.666666667 + 9 = 10.666666667
9 + 6v + v2 = 10.666666667

Factor a perfect square on the left side:
(v + 3)(v + 3) = 10.666666667

Calculate the square root of the right side: 3.265986324

Break this problem into two subproblems by setting 
(v + 3) equal to 3.265986324 and -3.265986324.

Subproblem 1
v + 3 = 3.265986324

Simplifying
v + 3 = 3.265986324

Reorder the terms:
3 + v = 3.265986324

Solving
3 + v = 3.265986324

Solving for variable 'v'.

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

Add '-3' to each side of the equation.
3 + -3 + v = 3.265986324 + -3

Combine like terms: 3 + -3 = 0
0 + v = 3.265986324 + -3
v = 3.265986324 + -3

Combine like terms: 3.265986324 + -3 = 0.265986324
v = 0.265986324

Simplifying
v = 0.265986324

Subproblem 2
v + 3 = -3.265986324

Simplifying
v + 3 = -3.265986324

Reorder the terms:
3 + v = -3.265986324

Solving
3 + v = -3.265986324

Solving for variable 'v'.

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

Add '-3' to each side of the equation.
3 + -3 + v = -3.265986324 + -3

Combine like terms: 3 + -3 = 0
0 + v = -3.265986324 + -3
v = -3.265986324 + -3

Combine like terms: -3.265986324 + -3 = -6.265986324
v = -6.265986324

Simplifying
v = -6.265986324

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.265986324, -6.265986324}
Solution
v = {0.265986324, -6.265986324}