8v^2-32v-40=0

Solution for 8v^2-32v-40=0 equation:

Simplifying
8v2 + -32v + -40 = 0

Reorder the terms:
-40 + -32v + 8v2 = 0

Solving
-40 + -32v + 8v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-5 + -4v + v2) = 0

Factor a trinomial.
8((-1 + -1v)(5 + -1v)) = 0

Ignore the factor 8.
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 '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-1, 5}