v^2=24-2v

Solution for v^2=24-2v equation:

Simplifying
v2 = 24 + -2v

Solving
v2 = 24 + -2v

Solving for variable 'v'.

Reorder the terms:
-24 + 2v + v2 = 24 + -2v + -24 + 2v

Reorder the terms:
-24 + 2v + v2 = 24 + -24 + -2v + 2v

Combine like terms: 24 + -24 = 0
-24 + 2v + v2 = 0 + -2v + 2v
-24 + 2v + v2 = -2v + 2v

Combine like terms: -2v + 2v = 0
-24 + 2v + v2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
v = {-6, 4}