20r^2+41r+20=0

Solution for 20r^2+41r+20=0 equation:

Simplifying
20r2 + 41r + 20 = 0

Reorder the terms:
20 + 41r + 20r2 = 0

Solving
20 + 41r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + 4r)(4 + 5r) = 0

Subproblem 1
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
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 = {-1.25, -0.8}