5n^2=-9n-4

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

Simplifying
5n2 = -9n + -4

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

Solving
5n2 = -4 + -9n

Solving for variable 'n'.

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

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

Combine like terms: -4 + 4 = 0
4 + 9n + 5n2 = 0 + -9n + 9n
4 + 9n + 5n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
4 + 9n + 5n2 = 0

Factor a trinomial.
(1 + n)(4 + 5n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + 5n)' equal to zero and attempt to solve:

Simplifying
4 + 5n = 0

Solving
4 + 5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5n = 0 + -4
5n = 0 + -4

Combine like terms: 0 + -4 = -4
5n = -4

Divide each side by '5'.
n = -0.8

Simplifying
n = -0.8
Solution
n = {-1, -0.8}