12v^2+v-6=0

Solution for 12v^2+v-6=0 equation:

Simplifying
12v2 + v + -6 = 0

Reorder the terms:
-6 + v + 12v2 = 0

Solving
-6 + v + 12v2 = 0

Solving for variable 'v'.

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

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 '(2 + -3v)' equal to zero and attempt to solve:

Simplifying
2 + -3v = 0

Solving
2 + -3v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3v = 0 + -2
-3v = 0 + -2

Combine like terms: 0 + -2 = -2
-3v = -2

Divide each side by '-3'.
v = 0.6666666667

Simplifying
v = 0.6666666667
Solution
v = {-0.75, 0.6666666667}