5n^2=-4+9n

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

Simplifying
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.
(4 + -5n)(1 + -1n) = 0

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

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

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