15b^2+31b-24=0

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

Simplifying
15b2 + 31b + -24 = 0

Reorder the terms:
-24 + 31b + 15b2 = 0

Solving
-24 + 31b + 15b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-8 + -3b = 0

Solving
-8 + -3b = 0

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

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

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

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

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

Simplifying
b = -2.666666667
Subproblem 2
Set the factor '(3 + -5b)' equal to zero and attempt to solve:

Simplifying
3 + -5b = 0

Solving
3 + -5b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5b = 0 + -3

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

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

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

Simplifying
b = 0.6
Solution
b = {-2.666666667, 0.6}