8b^2+31b-45=0

Solution for 8b^2+31b-45=0 equation:

Simplifying
8b2 + 31b + -45 = 0

Reorder the terms:
-45 + 31b + 8b2 = 0

Solving
-45 + 31b + 8b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -1b)(9 + -8b) = 0

Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve:

Simplifying
-5 + -1b = 0

Solving
-5 + -1b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1b = 0 + 5
-1b = 0 + 5

Combine like terms: 0 + 5 = 5
-1b = 5

Divide each side by '-1'.
b = -5

Simplifying
b = -5
Subproblem 2
Set the factor '(9 + -8b)' equal to zero and attempt to solve:

Simplifying
9 + -8b = 0

Solving
9 + -8b = 0

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

Add '-9' to each side of the equation.
9 + -9 + -8b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8b = 0 + -9
-8b = 0 + -9

Combine like terms: 0 + -9 = -9
-8b = -9

Divide each side by '-8'.
b = 1.125

Simplifying
b = 1.125
Solution
b = {-5, 1.125}