6v^2-72=-6v

Solution for 6v^2-72=-6v equation:

Simplifying
6v2 + -72 = -6v

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

Solving
-72 + 6v2 = -6v

Solving for variable 'v'.

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

Combine like terms: -6v + 6v = 0
-72 + 6v + 6v2 = 0

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

Factor a trinomial.
6((-4 + -1v)(3 + -1v)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + -1v)' equal to zero and attempt to solve:

Simplifying
-4 + -1v = 0

Solving
-4 + -1v = 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 + -1v = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1v = 0 + 4
-1v = 0 + 4

Combine like terms: 0 + 4 = 4
-1v = 4

Divide each side by '-1'.
v = -4

Simplifying
v = -4
Subproblem 2
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
Solution
v = {-4, 3}