24v^2-10v-6=0

Solution for 24v^2-10v-6=0 equation:

Simplifying
24v2 + -10v + -6 = 0

Reorder the terms:
-6 + -10v + 24v2 = 0

Solving
-6 + -10v + 24v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5v + 12v2) = 0

Factor a trinomial.
2((-1 + -3v)(3 + -4v)) = 0

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

Simplifying
-1 + -3v = 0

Solving
-1 + -3v = 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 + -3v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3v = 0 + 1
-3v = 0 + 1

Combine like terms: 0 + 1 = 1
-3v = 1

Divide each side by '-3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Subproblem 2
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
Solution
v = {-0.3333333333, 0.75}