6r^2-11r-30=0

Solution for 6r^2-11r-30=0 equation:

Simplifying
6r2 + -11r + -30 = 0

Reorder the terms:
-30 + -11r + 6r2 = 0

Solving
-30 + -11r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -2r)(10 + -3r) = 0

Subproblem 1
Set the factor '(-3 + -2r)' equal to zero and attempt to solve:

Simplifying
-3 + -2r = 0

Solving
-3 + -2r = 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 + -2r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2r = 0 + 3
-2r = 0 + 3

Combine like terms: 0 + 3 = 3
-2r = 3

Divide each side by '-2'.
r = -1.5

Simplifying
r = -1.5
Subproblem 2
Set the factor '(10 + -3r)' equal to zero and attempt to solve:

Simplifying
10 + -3r = 0

Solving
10 + -3r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3r = 0 + -10
-3r = 0 + -10

Combine like terms: 0 + -10 = -10
-3r = -10

Divide each side by '-3'.
r = 3.333333333

Simplifying
r = 3.333333333
Solution
r = {-1.5, 3.333333333}