6v^2+66v-72=0

Solution for 6v^2+66v-72=0 equation:

Simplifying
6v2 + 66v + -72 = 0

Reorder the terms:
-72 + 66v + 6v2 = 0

Solving
-72 + 66v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + 11v + v2) = 0

Factor a trinomial.
6((-12 + -1v)(1 + -1v)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-12 + -1v)' equal to zero and attempt to solve:

Simplifying
-12 + -1v = 0

Solving
-12 + -1v = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1v = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1v = 0 + 12
-1v = 0 + 12

Combine like terms: 0 + 12 = 12
-1v = 12

Divide each side by '-1'.
v = -12

Simplifying
v = -12
Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

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

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

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

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

Simplifying
v = 1
Solution
v = {-12, 1}