40b^2-45b+5=0

Solution for 40b^2-45b+5=0 equation:

Simplifying
40b2 + -45b + 5 = 0

Reorder the terms:
5 + -45b + 40b2 = 0

Solving
5 + -45b + 40b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -9b + 8b2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -8b)' equal to zero and attempt to solve:

Simplifying
1 + -8b = 0

Solving
1 + -8b = 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 + -8b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8b = 0 + -1
-8b = 0 + -1

Combine like terms: 0 + -1 = -1
-8b = -1

Divide each side by '-8'.
b = 0.125

Simplifying
b = 0.125
Subproblem 2
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
Solution
b = {0.125, 1}