v^2-4v-21=-9

Solution for v^2-4v-21=-9 equation:

Simplifying
v2 + -4v + -21 = -9

Reorder the terms:
-21 + -4v + v2 = -9

Solving
-21 + -4v + v2 = -9

Solving for variable 'v'.

Reorder the terms:
-21 + 9 + -4v + v2 = -9 + 9

Combine like terms: -21 + 9 = -12
-12 + -4v + v2 = -9 + 9

Combine like terms: -9 + 9 = 0
-12 + -4v + v2 = 0

Factor a trinomial.
(-2 + -1v)(6 + -1v) = 0

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

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v = 0 + 2
-1v = 0 + 2

Combine like terms: 0 + 2 = 2
-1v = 2

Divide each side by '-1'.
v = -2

Simplifying
v = -2
Subproblem 2
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
Solution
v = {-2, 6}