4b^2+5b-9=0

Solution for 4b^2+5b-9=0 equation:

Simplifying
4b2 + 5b + -9 = 0

Reorder the terms:
-9 + 5b + 4b2 = 0

Solving
-9 + 5b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-9 + -4b)(1 + -1b) = 0

Subproblem 1
Set the factor '(-9 + -4b)' equal to zero and attempt to solve:

Simplifying
-9 + -4b = 0

Solving
-9 + -4b = 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 + -4b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4b = 0 + 9
-4b = 0 + 9

Combine like terms: 0 + 9 = 9
-4b = 9

Divide each side by '-4'.
b = -2.25

Simplifying
b = -2.25
Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1
Solution
b = {-2.25, 1}