20b^2+27b=-9

Solution for 20b^2+27b=-9 equation:

Simplifying
20b2 + 27b = -9

Reorder the terms:
27b + 20b2 = -9

Solving
27b + 20b2 = -9

Solving for variable 'b'.

Reorder the terms:
9 + 27b + 20b2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + 27b + 20b2 = 0

Factor a trinomial.
(3 + 4b)(3 + 5b) = 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 '(3 + 5b)' equal to zero and attempt to solve:

Simplifying
3 + 5b = 0

Solving
3 + 5b = 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 + 5b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5b = 0 + -3
5b = 0 + -3

Combine like terms: 0 + -3 = -3
5b = -3

Divide each side by '5'.
b = -0.6

Simplifying
b = -0.6
Solution
b = {-0.75, -0.6}