(5v+1)(4v-2)=0

Solution for (5v+1)(4v-2)=0 equation:

Simplifying
(5v + 1)(4v + -2) = 0

Reorder the terms:
(1 + 5v)(4v + -2) = 0

Reorder the terms:
(1 + 5v)(-2 + 4v) = 0

Multiply (1 + 5v) * (-2 + 4v)
(1(-2 + 4v) + 5v * (-2 + 4v)) = 0
((-2 * 1 + 4v * 1) + 5v * (-2 + 4v)) = 0
((-2 + 4v) + 5v * (-2 + 4v)) = 0
(-2 + 4v + (-2 * 5v + 4v * 5v)) = 0
(-2 + 4v + (-10v + 20v2)) = 0

Combine like terms: 4v + -10v = -6v
(-2 + -6v + 20v2) = 0

Solving
-2 + -6v + 20v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -3v + 10v2) = 0

Factor a trinomial.
2((-1 + -5v)(1 + -2v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -5v)' equal to zero and attempt to solve:

Simplifying
-1 + -5v = 0

Solving
-1 + -5v = 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 + -5v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5v = 0 + 1
-5v = 0 + 1

Combine like terms: 0 + 1 = 1
-5v = 1

Divide each side by '-5'.
v = -0.2

Simplifying
v = -0.2
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 = {-0.2, 0.5}