8v^2-21v-9=0

Solution for 8v^2-21v-9=0 equation:

Simplifying
8v2 + -21v + -9 = 0

Reorder the terms:
-9 + -21v + 8v2 = 0

Solving
-9 + -21v + 8v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-3 + -8v)(3 + -1v) = 0

Subproblem 1
Set the factor '(-3 + -8v)' equal to zero and attempt to solve:

Simplifying
-3 + -8v = 0

Solving
-3 + -8v = 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 + -8v = 0 + 3

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

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

Divide each side by '-8'.
v = -0.375

Simplifying
v = -0.375
Subproblem 2
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
Solution
v = {-0.375, 3}