2v^2-4v=48

Solution for 2v^2-4v=48 equation:

Simplifying
2v2 + -4v = 48

Reorder the terms:
-4v + 2v2 = 48

Solving
-4v + 2v2 = 48

Solving for variable 'v'.

Reorder the terms:
-48 + -4v + 2v2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -4v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -2v + v2) = 0

Factor a trinomial.
2((-4 + -1v)(6 + -1v)) = 0

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

Simplifying
-4 + -1v = 0

Solving
-4 + -1v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1v = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1v = 0 + 4
-1v = 0 + 4

Combine like terms: 0 + 4 = 4
-1v = 4

Divide each side by '-1'.
v = -4

Simplifying
v = -4
Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {-4, 6}