20r^2-31r-345=0

Solution for 20r^2-31r-345=0 equation:

Simplifying
20r2 + -31r + -345 = 0

Reorder the terms:
-345 + -31r + 20r2 = 0

Solving
-345 + -31r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-69 + -20r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-69 + -20r)' equal to zero and attempt to solve:

Simplifying
-69 + -20r = 0

Solving
-69 + -20r = 0

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

Add '69' to each side of the equation.
-69 + 69 + -20r = 0 + 69

Combine like terms: -69 + 69 = 0
0 + -20r = 0 + 69
-20r = 0 + 69

Combine like terms: 0 + 69 = 69
-20r = 69

Divide each side by '-20'.
r = -3.45

Simplifying
r = -3.45
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

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

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

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-3.45, 5}