4b^2-9b+5=0

Solution for 4b^2-9b+5=0 equation:

Simplifying
4b2 + -9b + 5 = 0

Reorder the terms:
5 + -9b + 4b2 = 0

Solving
5 + -9b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -1b)(5 + -4b) = 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 + -4b)' equal to zero and attempt to solve:

Simplifying
5 + -4b = 0

Solving
5 + -4b = 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 + -4b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4b = 0 + -5
-4b = 0 + -5

Combine like terms: 0 + -5 = -5
-4b = -5

Divide each side by '-4'.
b = 1.25

Simplifying
b = 1.25
Solution
b = {1, 1.25}