2r(5r-2)=0

Solution for 2r(5r-2)=0 equation:

Simplifying
2r(5r + -2) = 0

Reorder the terms:
2r(-2 + 5r) = 0
(-2 * 2r + 5r * 2r) = 0
(-4r + 10r2) = 0

Solving
-4r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-2 + 5r) = 0

Ignore the factor 2.
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 '(-2 + 5r)' equal to zero and attempt to solve:

Simplifying
-2 + 5r = 0

Solving
-2 + 5r = 0

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

Add '2' to each side of the equation.
-2 + 2 + 5r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5r = 0 + 2
5r = 0 + 2

Combine like terms: 0 + 2 = 2
5r = 2

Divide each side by '5'.
r = 0.4

Simplifying
r = 0.4
Solution
r = {0, 0.4}