2r(5r+3)=0

Solution for 2r(5r+3)=0 equation:

Simplifying
2r(5r + 3) = 0

Reorder the terms:
2r(3 + 5r) = 0
(3 * 2r + 5r * 2r) = 0
(6r + 10r2) = 0

Solving
6r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(3 + 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 '(3 + 5r)' equal to zero and attempt to solve:

Simplifying
3 + 5r = 0

Solving
3 + 5r = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5r = 0 + -3
5r = 0 + -3

Combine like terms: 0 + -3 = -3
5r = -3

Divide each side by '5'.
r = -0.6

Simplifying
r = -0.6
Solution
r = {0, -0.6}