(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 = 11v
(-3 + 11v + 4v2) = 0

Solving
-3 + 11v + 4v2 = 0

Solving for variable 'v'.

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

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

Simplifying
-3 + -1v = 0

Solving
-3 + -1v = 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 + -1v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1v = 0 + 3
-1v = 0 + 3

Combine like terms: 0 + 3 = 3
-1v = 3

Divide each side by '-1'.
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}