20r^2+19r+3=0

Solution for 20r^2+19r+3=0 equation:

Simplifying
20r2 + 19r + 3 = 0

Reorder the terms:
3 + 19r + 20r2 = 0

Solving
3 + 19r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + 4r)(1 + 5r) = 0

Subproblem 1
Set the factor '(3 + 4r)' equal to zero and attempt to solve:

Simplifying
3 + 4r = 0

Solving
3 + 4r = 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 + 4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4r = 0 + -3
4r = 0 + -3

Combine like terms: 0 + -3 = -3
4r = -3

Divide each side by '4'.
r = -0.75

Simplifying
r = -0.75
Subproblem 2
Set the factor '(1 + 5r)' equal to zero and attempt to solve:

Simplifying
1 + 5r = 0

Solving
1 + 5r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5r = 0 + -1
5r = 0 + -1

Combine like terms: 0 + -1 = -1
5r = -1

Divide each side by '5'.
r = -0.2

Simplifying
r = -0.2
Solution
r = {-0.75, -0.2}