r(5r+4)=0

Solution for r(5r+4)=0 equation:

Simplifying
r(5r + 4) = 0

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

Solving
4r + 5r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(4 + 5r) = 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 '(4 + 5r)' equal to zero and attempt to solve:

Simplifying
4 + 5r = 0

Solving
4 + 5r = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5r = 0 + -4
5r = 0 + -4

Combine like terms: 0 + -4 = -4
5r = -4

Divide each side by '5'.
r = -0.8

Simplifying
r = -0.8
Solution
r = {0, -0.8}