5n^2-8n+9=6

Solution for 5n^2-8n+9=6 equation:

Simplifying
5n2 + -8n + 9 = 6

Reorder the terms:
9 + -8n + 5n2 = 6

Solving
9 + -8n + 5n2 = 6

Solving for variable 'n'.

Reorder the terms:
9 + -6 + -8n + 5n2 = 6 + -6

Combine like terms: 9 + -6 = 3
3 + -8n + 5n2 = 6 + -6

Combine like terms: 6 + -6 = 0
3 + -8n + 5n2 = 0

Factor a trinomial.
(3 + -5n)(1 + -1n) = 0

Subproblem 1
Set the factor '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

Solving
3 + -5n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5n = 0 + -3
-5n = 0 + -3

Combine like terms: 0 + -3 = -3
-5n = -3

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
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 = {0.6, 1}