v^2+12v-19=-6

Solution for v^2+12v-19=-6 equation:

Simplifying
v2 + 12v + -19 = -6

Reorder the terms:
-19 + 12v + v2 = -6

Solving
-19 + 12v + v2 = -6

Solving for variable 'v'.

Reorder the terms:
-19 + 6 + 12v + v2 = -6 + 6

Combine like terms: -19 + 6 = -13
-13 + 12v + v2 = -6 + 6

Combine like terms: -6 + 6 = 0
-13 + 12v + v2 = 0

Factor a trinomial.
(-13 + -1v)(1 + -1v) = 0

Subproblem 1
Set the factor '(-13 + -1v)' equal to zero and attempt to solve:

Simplifying
-13 + -1v = 0

Solving
-13 + -1v = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1v = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1v = 0 + 13
-1v = 0 + 13

Combine like terms: 0 + 13 = 13
-1v = 13

Divide each side by '-1'.
v = -13

Simplifying
v = -13
Subproblem 2
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
Solution
v = {-13, 1}