10n^2-59n+45=0

Solution for 10n^2-59n+45=0 equation:

Simplifying
10n2 + -59n + 45 = 0

Reorder the terms:
45 + -59n + 10n2 = 0

Solving
45 + -59n + 10n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(9 + -10n)(5 + -1n) = 0

Subproblem 1
Set the factor '(9 + -10n)' equal to zero and attempt to solve:

Simplifying
9 + -10n = 0

Solving
9 + -10n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -10n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -10n = 0 + -9
-10n = 0 + -9

Combine like terms: 0 + -9 = -9
-10n = -9

Divide each side by '-10'.
n = 0.9

Simplifying
n = 0.9
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.9, 5}