45b^2-48b+12=0

Solution for 45b^2-48b+12=0 equation:

Simplifying
45b2 + -48b + 12 = 0

Reorder the terms:
12 + -48b + 45b2 = 0

Solving
12 + -48b + 45b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -16b + 15b2) = 0

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

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

Simplifying
2 + -5b = 0

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

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

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

Divide each side by '-5'.
b = 0.4

Simplifying
b = 0.4
Subproblem 2
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
Solution
b = {0.4, 0.6666666667}