30r^2+r-20=0

Solution for 30r^2+r-20=0 equation:

Simplifying
30r2 + r + -20 = 0

Reorder the terms:
-20 + r + 30r2 = 0

Solving
-20 + r + 30r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -6r)(4 + -5r) = 0

Subproblem 1
Set the factor '(-5 + -6r)' equal to zero and attempt to solve:

Simplifying
-5 + -6r = 0

Solving
-5 + -6r = 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 + -6r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6r = 0 + 5
-6r = 0 + 5

Combine like terms: 0 + 5 = 5
-6r = 5

Divide each side by '-6'.
r = -0.8333333333

Simplifying
r = -0.8333333333
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 = {-0.8333333333, 0.8}