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

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

Simplifying
(6v + 3)(v + 1) = 0

Reorder the terms:
(3 + 6v)(v + 1) = 0

Reorder the terms:
(3 + 6v)(1 + v) = 0

Multiply (3 + 6v) * (1 + v)
(3(1 + v) + 6v * (1 + v)) = 0
((1 * 3 + v * 3) + 6v * (1 + v)) = 0
((3 + 3v) + 6v * (1 + v)) = 0
(3 + 3v + (1 * 6v + v * 6v)) = 0
(3 + 3v + (6v + 6v2)) = 0

Combine like terms: 3v + 6v = 9v
(3 + 9v + 6v2) = 0

Solving
3 + 9v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3v + 2v2) = 0

Factor a trinomial.
3((1 + v)(1 + 2v)) = 0

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

Simplifying
1 + v = 0

Solving
1 + v = 0

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

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

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

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

Simplifying
v = -1
Subproblem 2
Set the factor '(1 + 2v)' equal to zero and attempt to solve:

Simplifying
1 + 2v = 0

Solving
1 + 2v = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2v = 0 + -1
2v = 0 + -1

Combine like terms: 0 + -1 = -1
2v = -1

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {-1, -0.5}