24v^2-9v+32v-12=0

Solution for 24v^2-9v+32v-12=0 equation:

Simplifying
24v2 + -9v + 32v + -12 = 0

Reorder the terms:
-12 + -9v + 32v + 24v2 = 0

Combine like terms: -9v + 32v = 23v
-12 + 23v + 24v2 = 0

Solving
-12 + 23v + 24v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-4 + -3v)(3 + -8v) = 0

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

Simplifying
-4 + -3v = 0

Solving
-4 + -3v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3v = 0 + 4

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

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

Divide each side by '-3'.
v = -1.333333333

Simplifying
v = -1.333333333
Subproblem 2
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
Solution
v = {-1.333333333, 0.375}