v^2-6v-109=3

Solution for v^2-6v-109=3 equation:

Simplifying
v2 + -6v + -109 = 3

Reorder the terms:
-109 + -6v + v2 = 3

Solving
-109 + -6v + v2 = 3

Solving for variable 'v'.

Reorder the terms:
-109 + -3 + -6v + v2 = 3 + -3

Combine like terms: -109 + -3 = -112
-112 + -6v + v2 = 3 + -3

Combine like terms: 3 + -3 = 0
-112 + -6v + v2 = 0

Factor a trinomial.
(-8 + -1v)(14 + -1v) = 0

Subproblem 1
Set the factor '(-8 + -1v)' equal to zero and attempt to solve:

Simplifying
-8 + -1v = 0

Solving
-8 + -1v = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1v = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1v = 0 + 8
-1v = 0 + 8

Combine like terms: 0 + 8 = 8
-1v = 8

Divide each side by '-1'.
v = -8

Simplifying
v = -8
Subproblem 2
Set the factor '(14 + -1v)' equal to zero and attempt to solve:

Simplifying
14 + -1v = 0

Solving
14 + -1v = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1v = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1v = 0 + -14
-1v = 0 + -14

Combine like terms: 0 + -14 = -14
-1v = -14

Divide each side by '-1'.
v = 14

Simplifying
v = 14
Solution
v = {-8, 14}