r(4r-1)=0

Solution for r(4r-1)=0 equation:

Simplifying
r(4r + -1) = 0

Reorder the terms:
r(-1 + 4r) = 0
(-1 * r + 4r * r) = 0
(-1r + 4r2) = 0

Solving
-1r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-1 + 4r) = 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 + 4r)' equal to zero and attempt to solve:

Simplifying
-1 + 4r = 0

Solving
-1 + 4r = 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 + 4r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4r = 0 + 1
4r = 0 + 1

Combine like terms: 0 + 1 = 1
4r = 1

Divide each side by '4'.
r = 0.25

Simplifying
r = 0.25
Solution
r = {0, 0.25}