6(v+1)(v+3)+(v+3)=6(v+1)

Solution for 6(v+1)(v+3)+(v+3)=6(v+1) equation:

Simplifying
6(v + 1)(v + 3) + (v + 3) = 6(v + 1)

Reorder the terms:
6(1 + v)(v + 3) + (v + 3) = 6(v + 1)

Reorder the terms:
6(1 + v)(3 + v) + (v + 3) = 6(v + 1)

Multiply (1 + v) * (3 + v)
6(1(3 + v) + v(3 + v)) + (v + 3) = 6(v + 1)
6((3 * 1 + v * 1) + v(3 + v)) + (v + 3) = 6(v + 1)
6((3 + 1v) + v(3 + v)) + (v + 3) = 6(v + 1)
6(3 + 1v + (3 * v + v * v)) + (v + 3) = 6(v + 1)
6(3 + 1v + (3v + v2)) + (v + 3) = 6(v + 1)

Combine like terms: 1v + 3v = 4v
6(3 + 4v + v2) + (v + 3) = 6(v + 1)
(3 * 6 + 4v * 6 + v2 * 6) + (v + 3) = 6(v + 1)
(18 + 24v + 6v2) + (v + 3) = 6(v + 1)

Reorder the terms:
18 + 24v + 6v2 + (3 + v) = 6(v + 1)

Remove parenthesis around (3 + v)
18 + 24v + 6v2 + 3 + v = 6(v + 1)

Reorder the terms:
18 + 3 + 24v + v + 6v2 = 6(v + 1)

Combine like terms: 18 + 3 = 21
21 + 24v + v + 6v2 = 6(v + 1)

Combine like terms: 24v + v = 25v
21 + 25v + 6v2 = 6(v + 1)

Reorder the terms:
21 + 25v + 6v2 = 6(1 + v)
21 + 25v + 6v2 = (1 * 6 + v * 6)
21 + 25v + 6v2 = (6 + 6v)

Solving
21 + 25v + 6v2 = 6 + 6v

Solving for variable 'v'.

Reorder the terms:
21 + -6 + 25v + -6v + 6v2 = 6 + 6v + -6 + -6v

Combine like terms: 21 + -6 = 15
15 + 25v + -6v + 6v2 = 6 + 6v + -6 + -6v

Combine like terms: 25v + -6v = 19v
15 + 19v + 6v2 = 6 + 6v + -6 + -6v

Reorder the terms:
15 + 19v + 6v2 = 6 + -6 + 6v + -6v

Combine like terms: 6 + -6 = 0
15 + 19v + 6v2 = 0 + 6v + -6v
15 + 19v + 6v2 = 6v + -6v

Combine like terms: 6v + -6v = 0
15 + 19v + 6v2 = 0

Factor a trinomial.
(5 + 3v)(3 + 2v) = 0

Subproblem 1
Set the factor '(5 + 3v)' equal to zero and attempt to solve:

Simplifying
5 + 3v = 0

Solving
5 + 3v = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3v = 0 + -5
3v = 0 + -5

Combine like terms: 0 + -5 = -5
3v = -5

Divide each side by '3'.
v = -1.666666667

Simplifying
v = -1.666666667
Subproblem 2
Set the factor '(3 + 2v)' equal to zero and attempt to solve:

Simplifying
3 + 2v = 0

Solving
3 + 2v = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2v = 0 + -3
2v = 0 + -3

Combine like terms: 0 + -3 = -3
2v = -3

Divide each side by '2'.
v = -1.5

Simplifying
v = -1.5
Solution
v = {-1.666666667, -1.5}