-8v^2-51v-18=0

Solution for -8v^2-51v-18=0 equation:

Simplifying
-8v2 + -51v + -18 = 0

Reorder the terms:
-18 + -51v + -8v2 = 0

Solving
-18 + -51v + -8v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 51v + 8v2) = 0

Factor a trinomial.
-1((6 + v)(3 + 8v)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Subproblem 2
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
Solution
v = {-6, -0.375}