(-4v+3)(8v+6)=0

Solution for (-4v+3)(8v+6)=0 equation:

Simplifying
(-4v + 3)(8v + 6) = 0

Reorder the terms:
(3 + -4v)(8v + 6) = 0

Reorder the terms:
(3 + -4v)(6 + 8v) = 0

Multiply (3 + -4v) * (6 + 8v)
(3(6 + 8v) + -4v * (6 + 8v)) = 0
((6 * 3 + 8v * 3) + -4v * (6 + 8v)) = 0
((18 + 24v) + -4v * (6 + 8v)) = 0
(18 + 24v + (6 * -4v + 8v * -4v)) = 0
(18 + 24v + (-24v + -32v2)) = 0

Combine like terms: 24v + -24v = 0
(18 + 0 + -32v2) = 0
(18 + -32v2) = 0

Solving
18 + -32v2 = 0

Solving for variable 'v'.

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

Add '-18' to each side of the equation.
18 + -18 + -32v2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -32v2 = 0 + -18
-32v2 = 0 + -18

Combine like terms: 0 + -18 = -18
-32v2 = -18

Divide each side by '-32'.
v2 = 0.5625

Simplifying
v2 = 0.5625

Take the square root of each side:
v = {-0.75, 0.75}