5n^2=44n-32

Solution for 5n^2=44n-32 equation:

Simplifying
5n2 = 44n + -32

Reorder the terms:
5n2 = -32 + 44n

Solving
5n2 = -32 + 44n

Solving for variable 'n'.

Reorder the terms:
32 + -44n + 5n2 = -32 + 44n + 32 + -44n

Reorder the terms:
32 + -44n + 5n2 = -32 + 32 + 44n + -44n

Combine like terms: -32 + 32 = 0
32 + -44n + 5n2 = 0 + 44n + -44n
32 + -44n + 5n2 = 44n + -44n

Combine like terms: 44n + -44n = 0
32 + -44n + 5n2 = 0

Factor a trinomial.
(4 + -5n)(8 + -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 '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {0.8, 8}