r^2-4rt+4t^2=0

Solution for r^2-4rt+4t^2=0 equation:

Simplifying
r2 + -4rt + 4t2 = 0

Reorder the terms:
-4rt + r2 + 4t2 = 0

Solving
-4rt + r2 + 4t2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -2t)(r + -2t) = 0

Subproblem 1
Set the factor '(r + -2t)' equal to zero and attempt to solve:

Simplifying
r + -2t = 0

Solving
r + -2t = 0

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

Add '2t' to each side of the equation.
r + -2t + 2t = 0 + 2t

Combine like terms: -2t + 2t = 0
r + 0 = 0 + 2t
r = 0 + 2t
Remove the zero:
r = 2t

Simplifying
r = 2t
Subproblem 2
Set the factor '(r + -2t)' equal to zero and attempt to solve:

Simplifying
r + -2t = 0

Solving
r + -2t = 0

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

Add '2t' to each side of the equation.
r + -2t + 2t = 0 + 2t

Combine like terms: -2t + 2t = 0
r + 0 = 0 + 2t
r = 0 + 2t
Remove the zero:
r = 2t

Simplifying
r = 2t
Solution
r = {2t, 2t}