8v^2+16v+1=-5

Solution for 8v^2+16v+1=-5 equation:

Simplifying
8v2 + 16v + 1 = -5

Reorder the terms:
1 + 16v + 8v2 = -5

Solving
1 + 16v + 8v2 = -5

Solving for variable 'v'.

Reorder the terms:
1 + 5 + 16v + 8v2 = -5 + 5

Combine like terms: 1 + 5 = 6
6 + 16v + 8v2 = -5 + 5

Combine like terms: -5 + 5 = 0
6 + 16v + 8v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 8v + 4v2) = 0

Factor a trinomial.
2((3 + 2v)(1 + 2v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 2v)' equal to zero and attempt to solve:

Simplifying
3 + 2v = 0

Solving
3 + 2v = 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 + 2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2v = 0 + -3
2v = 0 + -3

Combine like terms: 0 + -3 = -3
2v = -3

Divide each side by '2'.
v = -1.5

Simplifying
v = -1.5
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 = {-1.5, -0.5}