10b^2=27b-18

Solution for 10b^2=27b-18 equation:

Simplifying
10b2 = 27b + -18

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

Solving
10b2 = -18 + 27b

Solving for variable 'b'.

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

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

Combine like terms: -18 + 18 = 0
18 + -27b + 10b2 = 0 + 27b + -27b
18 + -27b + 10b2 = 27b + -27b

Combine like terms: 27b + -27b = 0
18 + -27b + 10b2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
b = {1.2, 1.5}