9n^2=5+4n

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

Simplifying
9n2 = 5 + 4n

Solving
9n2 = 5 + 4n

Solving for variable 'n'.

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

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

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

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

Factor a trinomial.
(-5 + -9n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -9n)' equal to zero and attempt to solve:

Simplifying
-5 + -9n = 0

Solving
-5 + -9n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -9n = 0 + 5

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

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

Divide each side by '-9'.
n = -0.5555555556

Simplifying
n = -0.5555555556
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 = {-0.5555555556, 1}