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

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

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

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

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