-4n^2+5n+9=0

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

Simplifying
-4n2 + 5n + 9 = 0

Reorder the terms:
9 + 5n + -4n2 = 0

Solving
9 + 5n + -4n2 = 0

Solving for variable 'n'.

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

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

Simplifying
9 + -4n = 0

Solving
9 + -4n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4n = 0 + -9

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

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

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

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

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