5n^2-4n-105=-9

Solution for 5n^2-4n-105=-9 equation:

Simplifying
5n2 + -4n + -105 = -9

Reorder the terms:
-105 + -4n + 5n2 = -9

Solving
-105 + -4n + 5n2 = -9

Solving for variable 'n'.

Reorder the terms:
-105 + 9 + -4n + 5n2 = -9 + 9

Combine like terms: -105 + 9 = -96
-96 + -4n + 5n2 = -9 + 9

Combine like terms: -9 + 9 = 0
-96 + -4n + 5n2 = 0

Factor a trinomial.
(-4 + -1n)(24 + -5n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 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 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(24 + -5n)' equal to zero and attempt to solve:

Simplifying
24 + -5n = 0

Solving
24 + -5n = 0

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

Add '-24' to each side of the equation.
24 + -24 + -5n = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -5n = 0 + -24
-5n = 0 + -24

Combine like terms: 0 + -24 = -24
-5n = -24

Divide each side by '-5'.
n = 4.8

Simplifying
n = 4.8
Solution
n = {-4, 4.8}