4v^2+12v+8=0

Solution for 4v^2+12v+8=0 equation:

Simplifying
4v2 + 12v + 8 = 0

Reorder the terms:
8 + 12v + 4v2 = 0

Solving
8 + 12v + 4v2 = 0

Solving for variable 'v'.

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

Factor a trinomial.
4((2 + v)(1 + v)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + v)' equal to zero and attempt to solve:

Simplifying
2 + v = 0

Solving
2 + v = 0

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

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

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

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

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

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Solution
v = {-2, -1}