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

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

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

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

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

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

Solving
2 + 2v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + v + -2v2) = 0

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

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

Simplifying
1 + -1v = 0

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

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

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

Divide each side by '-1'.
v = 1

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

Simplifying
1 + 2v = 0

Solving
1 + 2v = 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 + 2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2v = 0 + -1
2v = 0 + -1

Combine like terms: 0 + -1 = -1
2v = -1

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {1, -0.5}