16b^2-40b+9=0

Solution for 16b^2-40b+9=0 equation:

Simplifying
16b2 + -40b + 9 = 0

Reorder the terms:
9 + -40b + 16b2 = 0

Solving
9 + -40b + 16b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -4b)(9 + -4b) = 0

Subproblem 1
Set the factor '(1 + -4b)' equal to zero and attempt to solve:

Simplifying
1 + -4b = 0

Solving
1 + -4b = 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 + -4b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4b = 0 + -1
-4b = 0 + -1

Combine like terms: 0 + -1 = -1
-4b = -1

Divide each side by '-4'.
b = 0.25

Simplifying
b = 0.25
Subproblem 2
Set the factor '(9 + -4b)' equal to zero and attempt to solve:

Simplifying
9 + -4b = 0

Solving
9 + -4b = 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 + -4b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4b = 0 + -9
-4b = 0 + -9

Combine like terms: 0 + -9 = -9
-4b = -9

Divide each side by '-4'.
b = 2.25

Simplifying
b = 2.25
Solution
b = {0.25, 2.25}