v^2-12v-108=0

Solution for v^2-12v-108=0 equation:

Simplifying
v2 + -12v + -108 = 0

Reorder the terms:
-108 + -12v + v2 = 0

Solving
-108 + -12v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-6 + -1v)(18 + -1v) = 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 '(18 + -1v)' equal to zero and attempt to solve:

Simplifying
18 + -1v = 0

Solving
18 + -1v = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1v = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1v = 0 + -18
-1v = 0 + -18

Combine like terms: 0 + -18 = -18
-1v = -18

Divide each side by '-1'.
v = 18

Simplifying
v = 18
Solution
v = {-6, 18}