(4v-1)(2-v)=0

Solution for (4v-1)(2-v)=0 equation:

Simplifying
(4v + -1)(2 + -1v) = 0

Reorder the terms:
(-1 + 4v)(2 + -1v) = 0

Multiply (-1 + 4v) * (2 + -1v)
(-1(2 + -1v) + 4v * (2 + -1v)) = 0
((2 * -1 + -1v * -1) + 4v * (2 + -1v)) = 0
((-2 + 1v) + 4v * (2 + -1v)) = 0
(-2 + 1v + (2 * 4v + -1v * 4v)) = 0
(-2 + 1v + (8v + -4v2)) = 0

Combine like terms: 1v + 8v = 9v
(-2 + 9v + -4v2) = 0

Solving
-2 + 9v + -4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-2 + v)(1 + -4v) = 0

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

Simplifying
-2 + v = 0

Solving
-2 + v = 0

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

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

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

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

Simplifying
v = 2
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 = {2, 0.25}