15r^2+31r-24=0

Solution for 15r^2+31r-24=0 equation:

Simplifying
15r2 + 31r + -24 = 0

Reorder the terms:
-24 + 31r + 15r2 = 0

Solving
-24 + 31r + 15r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-8 + -3r)(3 + -5r) = 0

Subproblem 1
Set the factor '(-8 + -3r)' equal to zero and attempt to solve:

Simplifying
-8 + -3r = 0

Solving
-8 + -3r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3r = 0 + 8
-3r = 0 + 8

Combine like terms: 0 + 8 = 8
-3r = 8

Divide each side by '-3'.
r = -2.666666667

Simplifying
r = -2.666666667
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 = {-2.666666667, 0.6}