v^2-v-6=6

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

Simplifying
v2 + -1v + -6 = 6

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

Solving
-6 + -1v + v2 = 6

Solving for variable 'v'.

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

Combine like terms: -6 + -6 = -12
-12 + -1v + v2 = 6 + -6

Combine like terms: 6 + -6 = 0
-12 + -1v + v2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
v = {-3, 4}