(8v+3)(7v-1)=0

Solution for (8v+3)(7v-1)=0 equation:

Simplifying
(8v + 3)(7v + -1) = 0

Reorder the terms:
(3 + 8v)(7v + -1) = 0

Reorder the terms:
(3 + 8v)(-1 + 7v) = 0

Multiply (3 + 8v) * (-1 + 7v)
(3(-1 + 7v) + 8v * (-1 + 7v)) = 0
((-1 * 3 + 7v * 3) + 8v * (-1 + 7v)) = 0
((-3 + 21v) + 8v * (-1 + 7v)) = 0
(-3 + 21v + (-1 * 8v + 7v * 8v)) = 0
(-3 + 21v + (-8v + 56v2)) = 0

Combine like terms: 21v + -8v = 13v
(-3 + 13v + 56v2) = 0

Solving
-3 + 13v + 56v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-3 + -8v)(1 + -7v) = 0

Subproblem 1
Set the factor '(-3 + -8v)' equal to zero and attempt to solve:

Simplifying
-3 + -8v = 0

Solving
-3 + -8v = 0

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

Add '3' to each side of the equation.
-3 + 3 + -8v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8v = 0 + 3
-8v = 0 + 3

Combine like terms: 0 + 3 = 3
-8v = 3

Divide each side by '-8'.
v = -0.375

Simplifying
v = -0.375
Subproblem 2
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
Solution
v = {-0.375, 0.1428571429}