4rs^2-4rs+r=

Solution for 4rs^2-4rs+r= equation:

Simplifying
4rs2 + -4rs + r = 0

Reorder the terms:
r + -4rs + 4rs2 = 0

Solving
r + -4rs + 4rs2 = 0

Solving for variable 'r'.

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

Factor out the Greatest Common Factor (GCF), 'r'.
r(1 + -4s + 4s2) = 0

Factor a trinomial.
r((1 + -2s)(1 + -2s)) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(1 + -2s)' equal to zero and attempt to solve:

Simplifying
1 + -2s = 0

Solving
1 + -2s = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2s = 0 + -1
-2s = 0 + -1

Combine like terms: 0 + -1 = -1
-2s = -1

Add '2s' to each side of the equation.
-2s + 2s = -1 + 2s

Combine like terms: -2s + 2s = 0
0 = -1 + 2s

Simplifying
0 = -1 + 2s

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + -2s)' equal to zero and attempt to solve:

Simplifying
1 + -2s = 0

Solving
1 + -2s = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2s = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2s = 0 + -1
-2s = 0 + -1

Combine like terms: 0 + -1 = -1
-2s = -1

Add '2s' to each side of the equation.
-2s + 2s = -1 + 2s

Combine like terms: -2s + 2s = 0
0 = -1 + 2s

Simplifying
0 = -1 + 2s

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}