(-10b^2)+27b-18=0

Solution for (-10b^2)+27b-18=0 equation:

Simplifying
(-10b2) + 27b + -18 = 0

Reorder the terms:
-18 + 27b + (-10b2) = 0

Solving
-18 + 27b + (-10b2) = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + 2b)(6 + -5b) = 0

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

Simplifying
-3 + 2b = 0

Solving
-3 + 2b = 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 + 2b = 0 + 3

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

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

Divide each side by '2'.
b = 1.5

Simplifying
b = 1.5
Subproblem 2
Set the factor '(6 + -5b)' equal to zero and attempt to solve:

Simplifying
6 + -5b = 0

Solving
6 + -5b = 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 + -5b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5b = 0 + -6
-5b = 0 + -6

Combine like terms: 0 + -6 = -6
-5b = -6

Divide each side by '-5'.
b = 1.2

Simplifying
b = 1.2
Solution
b = {1.5, 1.2}