15r^2-31r-12=0

Solution for 15r^2-31r-12=0 equation:

Simplifying
15r2 + -31r + -12 = 0

Reorder the terms:
-12 + -31r + 15r2 = 0

Solving
-12 + -31r + 15r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -3r)(12 + -5r) = 0

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

Simplifying
-1 + -3r = 0

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

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

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

Divide each side by '-3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 2
Set the factor '(12 + -5r)' equal to zero and attempt to solve:

Simplifying
12 + -5r = 0

Solving
12 + -5r = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5r = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5r = 0 + -12
-5r = 0 + -12

Combine like terms: 0 + -12 = -12
-5r = -12

Divide each side by '-5'.
r = 2.4

Simplifying
r = 2.4
Solution
r = {-0.3333333333, 2.4}