(8v+6)(2v-7)=0

Solution for (8v+6)(2v-7)=0 equation:

Simplifying
(8v + 6)(2v + -7) = 0

Reorder the terms:
(6 + 8v)(2v + -7) = 0

Reorder the terms:
(6 + 8v)(-7 + 2v) = 0

Multiply (6 + 8v) * (-7 + 2v)
(6(-7 + 2v) + 8v * (-7 + 2v)) = 0
((-7 * 6 + 2v * 6) + 8v * (-7 + 2v)) = 0
((-42 + 12v) + 8v * (-7 + 2v)) = 0
(-42 + 12v + (-7 * 8v + 2v * 8v)) = 0
(-42 + 12v + (-56v + 16v2)) = 0

Combine like terms: 12v + -56v = -44v
(-42 + -44v + 16v2) = 0

Solving
-42 + -44v + 16v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -22v + 8v2) = 0

Factor a trinomial.
2((-3 + -4v)(7 + -2v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4v)' equal to zero and attempt to solve:

Simplifying
-3 + -4v = 0

Solving
-3 + -4v = 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 + -4v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4v = 0 + 3
-4v = 0 + 3

Combine like terms: 0 + 3 = 3
-4v = 3

Divide each side by '-4'.
v = -0.75

Simplifying
v = -0.75
Subproblem 2
Set the factor '(7 + -2v)' equal to zero and attempt to solve:

Simplifying
7 + -2v = 0

Solving
7 + -2v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2v = 0 + -7
-2v = 0 + -7

Combine like terms: 0 + -7 = -7
-2v = -7

Divide each side by '-2'.
v = 3.5

Simplifying
v = 3.5
Solution
v = {-0.75, 3.5}