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

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

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

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

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

Combine like terms: -1v + 12v = 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}