2r(4r+5)=

Solution for 2r(4r+5)= equation:

Simplifying
2r(4r + 5) = 0

Reorder the terms:
2r(5 + 4r) = 0
(5 * 2r + 4r * 2r) = 0
(10r + 8r2) = 0

Solving
10r + 8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(5 + 4r) = 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 '(5 + 4r)' equal to zero and attempt to solve:

Simplifying
5 + 4r = 0

Solving
5 + 4r = 0

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

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

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

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

Divide each side by '4'.
r = -1.25

Simplifying
r = -1.25
Solution
r = {0, -1.25}