6r^2-13r-15=0

Solution for 6r^2-13r-15=0 equation:

Simplifying
6r2 + -13r + -15 = 0

Reorder the terms:
-15 + -13r + 6r2 = 0

Solving
-15 + -13r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -6r)(3 + -1r) = 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 '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.8333333333, 3}