(3+v)(4v+1)=0

Solution for (3+v)(4v+1)=0 equation:

Simplifying
(3 + v)(4v + 1) = 0

Reorder the terms:
(3 + v)(1 + 4v) = 0

Multiply (3 + v) * (1 + 4v)
(3(1 + 4v) + v(1 + 4v)) = 0
((1 * 3 + 4v * 3) + v(1 + 4v)) = 0
((3 + 12v) + v(1 + 4v)) = 0
(3 + 12v + (1 * v + 4v * v)) = 0
(3 + 12v + (1v + 4v2)) = 0

Combine like terms: 12v + 1v = 13v
(3 + 13v + 4v2) = 0

Solving
3 + 13v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(3 + v)(1 + 4v) = 0

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

Simplifying
3 + v = 0

Solving
3 + v = 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 + v = 0 + -3

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

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

Simplifying
v = -3
Subproblem 2
Set the factor '(1 + 4v)' equal to zero and attempt to solve:

Simplifying
1 + 4v = 0

Solving
1 + 4v = 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 + 4v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4v = 0 + -1
4v = 0 + -1

Combine like terms: 0 + -1 = -1
4v = -1

Divide each side by '4'.
v = -0.25

Simplifying
v = -0.25
Solution
v = {-3, -0.25}