-v^2-6v+72=0

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

Simplifying
-1v2 + -6v + 72 = 0

Reorder the terms:
72 + -6v + -1v2 = 0

Solving
72 + -6v + -1v2 = 0

Solving for variable 'v'.

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

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

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Subproblem 2
Set the factor '(12 + v)' equal to zero and attempt to solve:

Simplifying
12 + v = 0

Solving
12 + v = 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 + v = 0 + -12

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

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

Simplifying
v = -12
Solution
v = {6, -12}