16b^2-48b+27=0

Solution for 16b^2-48b+27=0 equation:

Simplifying
16b2 + -48b + 27 = 0

Reorder the terms:
27 + -48b + 16b2 = 0

Solving
27 + -48b + 16b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + -4b)(9 + -4b) = 0

Subproblem 1
Set the factor '(3 + -4b)' equal to zero and attempt to solve:

Simplifying
3 + -4b = 0

Solving
3 + -4b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4b = 0 + -3
-4b = 0 + -3

Combine like terms: 0 + -3 = -3
-4b = -3

Divide each side by '-4'.
b = 0.75

Simplifying
b = 0.75
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 = {0.75, 2.25}