10b^2+33b-54=0

Solution for 10b^2+33b-54=0 equation:

Simplifying
10b2 + 33b + -54 = 0

Reorder the terms:
-54 + 33b + 10b2 = 0

Solving
-54 + 33b + 10b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-9 + -2b)(6 + -5b) = 0

Subproblem 1
Set the factor '(-9 + -2b)' equal to zero and attempt to solve:

Simplifying
-9 + -2b = 0

Solving
-9 + -2b = 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 + -2b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2b = 0 + 9
-2b = 0 + 9

Combine like terms: 0 + 9 = 9
-2b = 9

Divide each side by '-2'.
b = -4.5

Simplifying
b = -4.5
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 = {-4.5, 1.2}