8v^2+16v-10=0

Solution for 8v^2+16v-10=0 equation:

Simplifying
8v2 + 16v + -10 = 0

Reorder the terms:
-10 + 16v + 8v2 = 0

Solving
-10 + 16v + 8v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 8v + 4v2) = 0

Factor a trinomial.
2((-5 + -2v)(1 + -2v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -2v)' equal to zero and attempt to solve:

Simplifying
-5 + -2v = 0

Solving
-5 + -2v = 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 + -2v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2v = 0 + 5
-2v = 0 + 5

Combine like terms: 0 + 5 = 5
-2v = 5

Divide each side by '-2'.
v = -2.5

Simplifying
v = -2.5
Subproblem 2
Set the factor '(1 + -2v)' equal to zero and attempt to solve:

Simplifying
1 + -2v = 0

Solving
1 + -2v = 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 + -2v = 0 + -1

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

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

Divide each side by '-2'.
v = 0.5

Simplifying
v = 0.5
Solution
v = {-2.5, 0.5}