30r^2-13r-3=0

Solution for 30r^2-13r-3=0 equation:

Simplifying
30r2 + -13r + -3 = 0

Reorder the terms:
-3 + -13r + 30r2 = 0

Solving
-3 + -13r + 30r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -6r)(3 + -5r) = 0

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

Simplifying
-1 + -6r = 0

Solving
-1 + -6r = 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 + -6r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6r = 0 + 1
-6r = 0 + 1

Combine like terms: 0 + 1 = 1
-6r = 1

Divide each side by '-6'.
r = -0.1666666667

Simplifying
r = -0.1666666667
Subproblem 2
Set the factor '(3 + -5r)' equal to zero and attempt to solve:

Simplifying
3 + -5r = 0

Solving
3 + -5r = 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 + -5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5r = 0 + -3
-5r = 0 + -3

Combine like terms: 0 + -3 = -3
-5r = -3

Divide each side by '-5'.
r = 0.6

Simplifying
r = 0.6
Solution
r = {-0.1666666667, 0.6}