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

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

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

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

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