v^2=48-2v

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

Simplifying
v2 = 48 + -2v

Solving
v2 = 48 + -2v

Solving for variable 'v'.

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

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

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

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

Factor a trinomial.
(-8 + -1v)(6 + -1v) = 0

Subproblem 1
Set the factor '(-8 + -1v)' equal to zero and attempt to solve:

Simplifying
-8 + -1v = 0

Solving
-8 + -1v = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1v = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1v = 0 + 8
-1v = 0 + 8

Combine like terms: 0 + 8 = 8
-1v = 8

Divide each side by '-1'.
v = -8

Simplifying
v = -8
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 = {-8, 6}