v^2-2vp+p^2=0

Solution for v^2-2vp+p^2=0 equation:

Simplifying
v2 + -2vp + p2 = 0

Reorder the terms:
-2pv + p2 + v2 = 0

Solving
-2pv + p2 + v2 = 0

Solving for variable 'p'.

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

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

Simplifying
p + -1v = 0

Solving
p + -1v = 0

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

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

Combine like terms: -1v + v = 0
p + 0 = 0 + v
p = 0 + v
Remove the zero:
p = v

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

Simplifying
p + -1v = 0

Solving
p + -1v = 0

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

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

Combine like terms: -1v + v = 0
p + 0 = 0 + v
p = 0 + v
Remove the zero:
p = v

Simplifying
p = v
Solution
p = {v, v}