v^2-8v-12=-3

Solution for v^2-8v-12=-3 equation:

Simplifying
v2 + -8v + -12 = -3

Reorder the terms:
-12 + -8v + v2 = -3

Solving
-12 + -8v + v2 = -3

Solving for variable 'v'.

Reorder the terms:
-12 + 3 + -8v + v2 = -3 + 3

Combine like terms: -12 + 3 = -9
-9 + -8v + v2 = -3 + 3

Combine like terms: -3 + 3 = 0
-9 + -8v + v2 = 0

Factor a trinomial.
(-1 + -1v)(9 + -1v) = 0

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

Simplifying
-1 + -1v = 0

Solving
-1 + -1v = 0

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

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

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

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

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

Simplifying
v = -1
Subproblem 2
Set the factor '(9 + -1v)' equal to zero and attempt to solve:

Simplifying
9 + -1v = 0

Solving
9 + -1v = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1v = 0 + -9
-1v = 0 + -9

Combine like terms: 0 + -9 = -9
-1v = -9

Divide each side by '-1'.
v = 9

Simplifying
v = 9
Solution
v = {-1, 9}