v^2=32-4v

Solution for v^2=32-4v equation:

Simplifying
v2 = 32 + -4v

Solving
v2 = 32 + -4v

Solving for variable 'v'.

Reorder the terms:
-32 + 4v + v2 = 32 + -4v + -32 + 4v

Reorder the terms:
-32 + 4v + v2 = 32 + -32 + -4v + 4v

Combine like terms: 32 + -32 = 0
-32 + 4v + v2 = 0 + -4v + 4v
-32 + 4v + v2 = -4v + 4v

Combine like terms: -4v + 4v = 0
-32 + 4v + v2 = 0

Factor a trinomial.
(-8 + -1v)(4 + -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 '(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 = {-8, 4}