2b^2-3b-5=0

Solution for 2b^2-3b-5=0 equation:

Simplifying
2b2 + -3b + -5 = 0

Reorder the terms:
-5 + -3b + 2b2 = 0

Solving
-5 + -3b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -1b)(5 + -2b) = 0

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

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 0

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

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

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

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

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

Simplifying
b = -1
Subproblem 2
Set the factor '(5 + -2b)' equal to zero and attempt to solve:

Simplifying
5 + -2b = 0

Solving
5 + -2b = 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 + -2b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2b = 0 + -5
-2b = 0 + -5

Combine like terms: 0 + -5 = -5
-2b = -5

Divide each side by '-2'.
b = 2.5

Simplifying
b = 2.5
Solution
b = {-1, 2.5}