45b^2-105b+50=0

Solution for 45b^2-105b+50=0 equation:

Simplifying
45b2 + -105b + 50 = 0

Reorder the terms:
50 + -105b + 45b2 = 0

Solving
50 + -105b + 45b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(10 + -21b + 9b2) = 0

Factor a trinomial.
5((2 + -3b)(5 + -3b)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + -3b)' equal to zero and attempt to solve:

Simplifying
2 + -3b = 0

Solving
2 + -3b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3b = 0 + -2
-3b = 0 + -2

Combine like terms: 0 + -2 = -2
-3b = -2

Divide each side by '-3'.
b = 0.6666666667

Simplifying
b = 0.6666666667
Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve:

Simplifying
5 + -3b = 0

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

Combine like terms: 5 + -5 = 0
0 + -3b = 0 + -5
-3b = 0 + -5

Combine like terms: 0 + -5 = -5
-3b = -5

Divide each side by '-3'.
b = 1.666666667

Simplifying
b = 1.666666667
Solution
b = {0.6666666667, 1.666666667}