6v^2-4v-66=0

Solution for 6v^2-4v-66=0 equation:

Simplifying
6v2 + -4v + -66 = 0

Reorder the terms:
-66 + -4v + 6v2 = 0

Solving
-66 + -4v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -2v + 3v2) = 0

Factor a trinomial.
2((-3 + -1v)(11 + -3v)) = 0

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

Simplifying
-3 + -1v = 0

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

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

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

Divide each side by '-1'.
v = -3

Simplifying
v = -3
Subproblem 2
Set the factor '(11 + -3v)' equal to zero and attempt to solve:

Simplifying
11 + -3v = 0

Solving
11 + -3v = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3v = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3v = 0 + -11
-3v = 0 + -11

Combine like terms: 0 + -11 = -11
-3v = -11

Divide each side by '-3'.
v = 3.666666667

Simplifying
v = 3.666666667
Solution
v = {-3, 3.666666667}