(2v-1)(7v+1)=0

Solution for (2v-1)(7v+1)=0 equation:

Simplifying
(2v + -1)(7v + 1) = 0

Reorder the terms:
(-1 + 2v)(7v + 1) = 0

Reorder the terms:
(-1 + 2v)(1 + 7v) = 0

Multiply (-1 + 2v) * (1 + 7v)
(-1(1 + 7v) + 2v * (1 + 7v)) = 0
((1 * -1 + 7v * -1) + 2v * (1 + 7v)) = 0
((-1 + -7v) + 2v * (1 + 7v)) = 0
(-1 + -7v + (1 * 2v + 7v * 2v)) = 0
(-1 + -7v + (2v + 14v2)) = 0

Combine like terms: -7v + 2v = -5v
(-1 + -5v + 14v2) = 0

Solving
-1 + -5v + 14v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-1 + -7v)(1 + -2v) = 0

Subproblem 1
Set the factor '(-1 + -7v)' equal to zero and attempt to solve:

Simplifying
-1 + -7v = 0

Solving
-1 + -7v = 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 + -7v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7v = 0 + 1
-7v = 0 + 1

Combine like terms: 0 + 1 = 1
-7v = 1

Divide each side by '-7'.
v = -0.1428571429

Simplifying
v = -0.1428571429
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 = {-0.1428571429, 0.5}