4b^2-27b+18=0

Solution for 4b^2-27b+18=0 equation:

Simplifying
4b2 + -27b + 18 = 0

Reorder the terms:
18 + -27b + 4b2 = 0

Solving
18 + -27b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3 + -4b)(6 + -1b) = 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 '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {0.75, 6}