24=4(v+7)6v

Solution for 24=4(v+7)6v equation:

Simplifying
24 = 4(v + 7) * 6v

Reorder the terms:
24 = 4(7 + v) * 6v

Reorder the terms for easier multiplication:
24 = 4 * 6v(7 + v)

Multiply 4 * 6
24 = 24v(7 + v)
24 = (7 * 24v + v * 24v)
24 = (168v + 24v2)

Solving
24 = 168v + 24v2

Solving for variable 'v'.

Reorder the terms:
24 + -168v + -24v2 = 168v + -168v + 24v2 + -24v2

Combine like terms: 168v + -168v = 0
24 + -168v + -24v2 = 0 + 24v2 + -24v2
24 + -168v + -24v2 = 24v2 + -24v2

Combine like terms: 24v2 + -24v2 = 0
24 + -168v + -24v2 = 0

Factor out the Greatest Common Factor (GCF), '24'.
24(1 + -7v + -1v2) = 0

Ignore the factor 24.
Subproblem 1
Set the factor '(1 + -7v + -1v2)' equal to zero and attempt to solve:

Simplifying
1 + -7v + -1v2 = 0

Solving
1 + -7v + -1v2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 7v + v2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 7v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + 7v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 7v + v2 = 0 + 1
7v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
7v + v2 = 1

The v term is 7v.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7v + 12.25 + v2 = 1 + 12.25

Reorder the terms:
12.25 + 7v + v2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + 7v + v2 = 13.25

Factor a perfect square on the left side:
(v + 3.5)(v + 3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(v + 3.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
v + 3.5 = 3.640054945

Simplifying
v + 3.5 = 3.640054945

Reorder the terms:
3.5 + v = 3.640054945

Solving
3.5 + v = 3.640054945

Solving for variable 'v'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + v = 3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + v = 3.640054945 + -3.5
v = 3.640054945 + -3.5

Combine like terms: 3.640054945 + -3.5 = 0.140054945
v = 0.140054945

Simplifying
v = 0.140054945

Subproblem 2
v + 3.5 = -3.640054945

Simplifying
v + 3.5 = -3.640054945

Reorder the terms:
3.5 + v = -3.640054945

Solving
3.5 + v = -3.640054945

Solving for variable 'v'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + v = -3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + v = -3.640054945 + -3.5
v = -3.640054945 + -3.5

Combine like terms: -3.640054945 + -3.5 = -7.140054945
v = -7.140054945

Simplifying
v = -7.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.140054945, -7.140054945}
Solution
v = {0.140054945, -7.140054945}