10n^2-22n-24=0

Solution for 10n^2-22n-24=0 equation:

Simplifying
10n2 + -22n + -24 = 0

Reorder the terms:
-24 + -22n + 10n2 = 0

Solving
-24 + -22n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -11n + 5n2) = 0

Factor a trinomial.
2((-4 + -5n)(3 + -1n)) = 0

Ignore the factor 2.
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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-0.8, 3}