-4v^2+8v+12=0

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

Simplifying
-4v2 + 8v + 12 = 0

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

Solving
12 + 8v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 2v + -1v2) = 0

Factor a trinomial.
4((3 + -1v)(1 + v)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
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 = {3, -1}